While for the first three items there exists a vast literature and many techniques developed over the last two decades, the last problem of how to efficiently treat the time discretization has been widely ignored. The majority of the existing approaches just decouple the flow field from the geometry by a simple segregated approach, i.e. evaluating the geometric quantities from the previous time step. These strategy leads to a) a severe capillary CFL condition and b) is of first order in time at most. Existing semi-implicit discretizations exist that overcome problem a), but are still first order only and rather dissipative in certain situations.We compare different existing time discretization schemes for the fully coupled system of Navier-Stokes and the phase boundary condition. Time discretization might be semi-implicit, fully implicit or linearly implicit. The methods are applied to a simple test case where experimental order of convergence and numerical dissipation can be compared relatively easily.},
author = {Bänsch, Eberhard and Weller, Stephan},
booktitle = {ALGORITMY 2012, 19th Conference on Scientific Computing},
editor = {Angela Handlovicova, Zuzana Minarechova, Daniel Sevcovic},
faupublication = {yes},
pages = {331-341},
peerreviewed = {unknown},
title = {{A} comparison of several time discretization methods for free surface flows},
year = {2012}
}
@incollection{faucris.118336944,
address = {Rocquencourt},
author = {Bänsch, Eberhard},
booktitle = {Calcul d'erreur a posteriori et adaptation de maillage},
faupublication = {no},
note = {UnivIS-Import:2015-04-20:Pub.1995.nat.dma.lama3.meshre},
pages = {307-331},
peerreviewed = {unknown},
publisher = {INRIA},
title = {{Mesh} {Refinement} in {Two} and {Three} {Dimensions} {Calcul} d'erreur a posteriori et adaptation de maillage},
year = {1995}
}
@article{faucris.110746284,
abstract = {We consider a finite element discretization by the Taylor-Hood element for the stationary Stokes and Navier-Stokes equations with slip boundary condition. The slip boundary condition is enforced pointwise for nodal values of the velocity in boundary nodes. We prove optimal error estimates in the H^{1} and L^{2} norms for the velocity and pressure respectively.},
author = {Bänsch, Eberhard and Deckelnick, Klaus},
doi = {10.1051/m2an:1999126},
faupublication = {no},
journal = {Esaim-Mathematical Modelling and Numerical Analysis-Modelisation Mathematique Et Analyse Numerique},
keywords = {Error estimates; Finite elements; Navier-Stokes equations; Slip boundary condition; Stokes equations},
note = {UnivIS-Import:2015-03-05:Pub.1999.nat.dma.lama3.optima},
pages = {923-938},
peerreviewed = {Yes},
title = {{Optimal} {Error} {Estimates} for the {Stokes} and {Navier}-{Stokes} {Equations} with {Slip}-{Boundary} {Condition}},
volume = {33},
year = {1999}
}
@article{faucris.122819664,
author = {Bänsch, Eberhard and Schmidt, Alfred},
faupublication = {no},
journal = {Interfaces and Free Boundaries},
note = {UnivIS-Import:2015-03-09:Pub.2000.nat.dma.lama3.simula},
pages = {95-115},
peerreviewed = {Yes},
title = {{Simulation} of {Dendritic} {Crystal} {Growth} with {Thermal} {Convection}},
url = {http://www.ems-ph.org/journals/show_abstract.php?issn=1463-9963&vol=2&iss=1&rank=4},
volume = {2},
year = {2000}
}
@inproceedings{faucris.122788644,
address = {Berlin},
author = {Bänsch, Eberhard and Meincke, Oliver and Egbers, Christoph and Scurtu, Nicoleta},
booktitle = {Physics of Rotating Fluids},
faupublication = {no},
isbn = {3-540-67514-0},
note = {UnivIS-Import:2015-04-16:Pub.2000.nat.dma.lama3.taylor},
pages = {22-36},
peerreviewed = {unknown},
publisher = {Springer},
series = {Lecture Notes in Physics},
title = {{Taylor}-{Couette} {System} with {Asymmetric} {Boundary} {Conditions}},
venue = {Bremen},
volume = {549},
year = {2000}
}
@article{faucris.109614164,
abstract = {The determination of dislocation density and in particular the dislocation distribution in SiC wafers is of particular interest for SiC crystal growth development and production. We present an image recognition tool allowing the wafer analysis with specific needs for SiC. In the first stage of expansion, micropipes are selected and counted from SiC wafers that have been etched by KO},
author = {Karpinski, Harald and Sakwe, Aloysius and Fried, Michael J. and Bänsch, Eberhard and Wellmann, Peter},
doi = {10.4028/www.scientific.net/MSF.679-680.277},
faupublication = {yes},
journal = {Materials Science Forum},
keywords = {image analysis; dislocations; SiC; automatic detection},
pages = {277-281},
peerreviewed = {Yes},
title = {{Efficient} {Image} {Segmentation} for {Detection} of {Dislocations} in {High} {Resolution} {Light} {Microscope} {Images} of {SiC} {Wafers}},
volume = {679-680},
year = {2011}
}
@article{faucris.109633524,
author = {Prignitz, Rodolphe and Bänsch, Eberhard},
faupublication = {yes},
journal = {Kybernetika},
pages = {281-293},
peerreviewed = {Yes},
title = {{Numerical} simulation of suspension induced rheology},
volume = {46},
year = {2010}
}
@article{faucris.216820932,
abstract = {We present a mathematical model for convective transport in nanofluids including thermophoretic effects that is very similar to the celebrated model of Buongiorno [4]. Our model is thermodynamically consistent and consequently an energy estimate can be shown. We propose a semi–discretization in time that fully decouples the subproblems. Also for this semi–discrete problem an energy estimate can rigorously be shown. Based on this energy estimate it is proved that solutions of the semi–discrete problem converge to a weak solution of the system. We use the time discretization to define an effective, fully discrete finite element scheme. Simulations are performed for a nanofluid flowing through a heated long pipe. Careful inspection of the computational results reveal the mechanism of enhanced cooling properties of the nanofluid compared to the base fluid: The temperature gradient at the wall reduces the concentration of particles by thermophoresis. Thus, close to the wall, the viscosity is smaller compared to the bulk leading to an enhanced convective transport in the boundary layer.},
author = {Bänsch, Eberhard},
doi = {10.1016/j.jmaa.2019.04.002},
faupublication = {yes},
journal = {Journal of Mathematical Analysis and Applications},
keywords = {Energy estimate; Finite element; Heat transfer; Nanofluid; Thermophoresis; Weak solution},
note = {CRIS-Team Scopus Importer:2019-05-02},
peerreviewed = {Yes},
title = {{A} thermodynamically consistent model for convective transport in nanofluids: existence of weak solutions and fem computations},
year = {2019}
}
@article{faucris.204227950,
abstract = {We present a finite element method for simulating complex free surface flow. The mathematical model and the numerical method take into account two-phase non-isothermal flow of an incompressible liquid and a gas phase, capillary forces at the interface of both fluids, Marangoni effects due to temperature variation of the interface and mass transport across the interface by evaporation/condensation. The method is applied to two examples from microgravity research, for which experimental data are available.},
author = {Bänsch, Eberhard and Krahl, Rolf and Basting, Steffen},
doi = {10.3934/dcds.2015.35.2325},
faupublication = {yes},
journal = {Discrete and Continuous Dynamical Systems},
keywords = {Two-phase flow;evaporation;interface;finite elements},
pages = {2325-2347},
peerreviewed = {Yes},
title = {{NUMERICAL} {SIMULATION} {OF} {TWO}-{PHASE} {FLOWS} {WITH} {HEAT} {AND} {MASS} {TRANSFER}},
volume = {35},
year = {2015}
}
@article{faucris.121029084,
abstract = {The dynamic behavior of liquids in partly filled containers is influenced to a large extend by the angle between the gas-liquid phase boundary and the solid container wall at the contact line. This contact angle in turn is influenced by nonisothermal conditions. In the case of a cold liquid meniscus spreading over a hot solid wall, the contact angle apparently becomes significantly larger. In this paper we want to establish a quantitative equation for this enlargement, both from experimental and numerical data. Our findings can be used to build a subgrid model for computations, where the resolution is not sufficient to resolve the boundary layers. This might be the case for large containers which are exposed to low accelerations and where the contact angle boundary condition determines the position of the free surface. These types of computation are performed, for example, to solve propellant management problems in launcher and satellite tanks. In this application, the knowledge of the position of the free surface is very important for the withdrawal of liquid and the calculation of heat and mass transfer. © 2008 American Institute of Physics.},
author = {Krahl, Rolf and Gerstmann, Jens and Behruzi, Philipp and Bänsch, Eberhard and Dreyer, Michael E.},
doi = {10.1063/1.2899641},
faupublication = {yes},
journal = {Physics of Fluids},
keywords = {contact angle; capillary flows; contact lines; thermo-capillary flows},
note = {UnivIS-Import:2015-04-14:Pub.2008.nat.dma.lama3.depend},
pages = {042101},
peerreviewed = {unknown},
title = {{Dependency} of the {Apparent} {Contact} {Angle} on {Nonisothermal} {Conditions}},
url = {http://link.aip.org/link/?PHFLE6/20/042101/1},
volume = {20},
year = {2008}
}
@article{faucris.123264724,
abstract = {We consider hot forming processes, in which a metal solid body is deformed by several rolls in order to obtain a desired final shape. To minimize cutting scrap and to ensure that this shape satisfies the required tolerances as precisely as possible, we formulate an optimal control problem where we use the trajectories of the rolls as control functions. The deformation of the solid body is described through the basic equations of nonlinear continuum mechanics, which are here coupled with an elasto-viscoplastic material model based on a multiplicative split of the deformation gradient. We assume that the deformations of the rolls can be neglected, thus we add unilateral frictional contact boundary conditions, resulting in an evolutionary quasi-variational inclusion. The associated control-to-observation map is non-differentiable due to changes of state between elastic and plastic material behavior, contact and separation and stick and slip motion, yet we still want to apply gradient-based methods to solve the optimal control problem and therefore have to make sure that derivatives of cost functional and constraints exist. To resolve this issue, we first regularize all non-differentiabilities and subsequently apply the direct differentiation method to obtain sensitivity information. Finally, we formulate a suitable algorithm and discuss numerical results for a real-world example to illustrate its capability. (C) 2017 Elsevier B.V. All rights reserved.},
author = {Werner, Stefan and Stingl, Michael and Leugering, Günter},
doi = {10.1016/j.cma.2017.03.006},
faupublication = {yes},
journal = {Computer Methods in Applied Mechanics and Engineering},
keywords = {Optimal control; Regularization; Sensitivity analysis; Nonlinear continuum mechanics; Frictional contact; Elasto-viscoplasticity},
pages = {442-471},
peerreviewed = {Yes},
title = {{Model}-based control of dynamic frictional contact problems using the example of hot rolling},
volume = {319},
year = {2017}
}
@article{faucris.107961304,
author = {Schneider, Cornelia},
doi = {10.1002/mana.201010052},
faupublication = {no},
journal = {Mathematische Nachrichten},
pages = {572--586},
peerreviewed = {Yes},
title = {{Traces} of {Besov} and {Triebel}-{Lizorkin} spaces on domains},
volume = {284},
year = {2011}
}
@article{faucris.119808744,
abstract = {

One of the challenges in the numerics of free surface flows is the coupling of the flow field to the geometry of the domain. The most simple approach is an explicit decoupling, i.e. computing the flow field with geometrical information of a prior time step and then updating the geometry. This widely used approach leads to a severe CFL condition of the type , which may prescribe infinitesimally small time step sizes in the interesting case of a small Weber number (i.e. high surface tension). A semi-implicit approach utilizing the fact that , where *x*^{k} is a parametrization of the capillary boundary Γ, is also available [1]. This approach can be proven to be unconditionally stable but is of first order only. It also suffers from relatively strong numerical dissipation.

We present a fully implicit approach using a backward differentiation formula to achieve a time discretization method that is of second order and only minimally dissipative. A numerical example of an oscillating drop showing very low numerical dissipation and second order convergence as well as numerical evidence for the stability of the method is presented. Since the method requires the solution of a highly nonlinear coupled system, possible preconditioners for this system are discussed, including a lower order decoupling.

}, author = {Bänsch, Eberhard and Weller, Stephan}, doi = {10.1002/pamm.201110299}, faupublication = {yes}, journal = {Proceedings in Applied Mathematics and Mechanics}, pages = {619-620}, peerreviewed = {Yes}, title = {{Fully} implicit time discretization for a free surface flow problem}, volume = {11}, year = {2011} } @article{faucris.117254104, abstract = {The conductivity behavior of doped hydrocarbon systems is studied by applying impedance spectroscopy. In the case of 3,5-diisopropyl salicylato aluminum (III) the charge carriers are formed by dissociation of the compound and their concentration is proportional to the square root of the solute concentration. In hydrocarbon systems that consist of micelle forming compounds (sodium AOT/lecithin) a linear dependence of charge carrier concentration on solute concentration is observed in the concentration regime where micelles are present. The conduction mechanisms are studied by numerical solution of a Poisson-Nernst-Planck system that describes the charge transport. We follow two different approaches to extract the degree of micelle dissociation from the impedance data. Firstly, by computing the response of a linear approximation of the Poisson-Nernst-Planck model, and secondly by computing the fully nonlinear response from direct numerical simulations using finite elements. For high and moderate frequencies both approaches agree very well with the experimental data. For small frequencies the response becomes nonlinear and the concept of impedance fails. Furthermore, the numerically computed values for the degree of dissociation are of the same order of magnitude as the values obtained with classical formulas, but still differ by a factor of about 1/3. The direct numerical simulation allows new insight into the conduction mechanisms for different frequency regimes. © 2012 Elsevier Inc.}, author = {Peschka, Dirk and Schmidt, Jochen and Wagner, Barbara and Bänsch, Eberhard and Münch, Andreas and Peukert, Wolfgang and Prignitz, Rodolphe}, doi = {10.1016/j.jcis.2012.07.051}, faupublication = {yes}, journal = {Journal of Colloid S+D12486cience}, keywords = {Degree of dissociation; Direct numerical simulation; Electrochemical impedance spectroscopy; Finite element analysis; Poisson-Nernst-Planck model; Reverse micelles}, pages = {240-251}, peerreviewed = {unknown}, title = {{Conductivity} in nonpolar media: {Experimental} and numerical studies on sodium {AOT}-hexadecane, lecithin-hexadecane and aluminum({III})-3,5-diisopropyl salicylate-hexadecane systems}, volume = {386}, year = {2012} } @article{faucris.122193984, author = {Neuß, Nicolas}, doi = {10.1137/S0036142996310848}, faupublication = {no}, journal = {SIAM Journal on Numerical Analysis}, pages = {1201--1212}, peerreviewed = {Yes}, title = {{V}-{Cycle} {Convergence} with {Unsymmetric} {Smoothers} and {Application} to an {Anisotropic} {Model} {Problem}}, volume = {35}, year = {1998} } @article{faucris.120564224, abstract = {Surface diffusion is a (fourth order highly nonlinear) geometric driven motion of a surface with normal velocity proportional to the surface Laplacian of mean curvature. We present a novel variational formulation for parametric surfaces with or without boundaries. The method is semi-implicit, requires no explicit parametrization, and yields a linear system of elliptic PDE to solve at each time step. We next develop a finite element method, propose a Schur complement approach to solve the resulting linear systems, and show several significant simulations, some with pinch-off in finite time. We introduce a mesh regularization algorithm, which helps prevent mesh distortion, and discuss the use of time and space adaptivity to increase accuracy while reducing complexity. © 2004 Elsevier Inc. All rights reserved.}, author = {Bänsch, Eberhard and Morin, Pedro and Nochetto, Ricardo}, doi = {10.1016/j.jcp.2004.08.022}, faupublication = {yes}, journal = {Journal of Computational Physics}, keywords = {Finite elements; Fourth-order parabolic problem; Pinch-off; Schur complement; Smoothing effect; Surface diffusion}, note = {UnivIS-Import:2015-03-09:Pub.2005.nat.dma.lama3.afinit}, pages = {321-343}, peerreviewed = {Yes}, title = {{A} {Finite} {Element} {Method} for {Surface} {Diffusion}: the {Parametric} {Case}}, volume = {203}, year = {2005} } @article{faucris.111519584, author = {Bänsch, Eberhard and Tobiska, Lutz and Walkington, Noel J.}, faupublication = {yes}, journal = {Oberwolfach reports}, note = {UnivIS-Import:2015-03-09:Pub.2005.nat.dma.lama3.miniwo}, pages = {465-502}, peerreviewed = {No}, title = {{Mini}-{Workshop}: {Interface} {Problems} in {Computational} {Fluid} {Dynamics}}, url = {http://www.ems-ph.org/journals/show_abstract.php?issn=1660-8933&vol=2&iss=1&rank=8}, volume = {2}, year = {2005} } @article{faucris.110562364, abstract = {We introduce the coarsening of finite element computational grid strategy into the method proposed by Kačur and Mikula in [11] for the numerical solution of the Perona-Malik model modified in the sense of Catté, Lions, Morel and Coll. It improves the efficiency of the method, while the solution tends to be more flat during the selective smoothing process applied to the image. The numerical approximation consists of Rothe's method in time and linear finite elements on unstructured adaptively coarsened meshes in space. © Springer-Verlag 1997.}, author = {Bänsch, Eberhard and Mikula, Karol}, doi = {10.1007/s007910050005}, faupublication = {no}, journal = {Computing and Visualization in Science}, note = {UnivIS-Import:2015-03-05:Pub.1997.nat.dma.lama3.acoars}, pages = {53-61}, peerreviewed = {unknown}, title = {{A} {Coarsening} {Finite} {Element} {Strategy} in {Image} {Selective} {Smoothing}}, volume = {1}, year = {1997} } @inproceedings{faucris.109639464, author = {Krahl, Rolf and Adamov, Miroslav and Lozano Avilés, Miriam and Bänsch, Eberhard}, booktitle = {Proceedings of 3rd International Symposium on Two-Phase Flow Modelling and Experimentation}, date = {2004-09-22/2004-09-24}, faupublication = {no}, peerreviewed = {unknown}, title = {{A} model for two phase flow with evaporation}, venue = {Pisa}, year = {2004} } @article{faucris.200188889, author = {Büchs, Daniel and Ditter, Dominik and Henselmann, Klaus and Hering, Jörg and Götz, Michael}, faupublication = {yes}, journal = {Zeitschrift für Corporate Governance}, pages = {101-106}, peerreviewed = {unknown}, title = {{Directors}' {Dealings} am deutschen {Kapitalmarkt}}, year = {2016} } @article{faucris.204228220, abstract = {We present a finite element method for the simulation of all relevant processes of the evaporation of a liquid droplet suspended in an acoustic levitation device. The mathematical model and the numerical implementation take into account heat and mass transfer across the interface between the liquid and gaseous phase and the influence of acoustic streaming on this process, as well as the displacement and deformation of the droplet due to acoustic radiation pressure. We apply this numerical method to several theoretical and experimental examples and compare our results with the well-known d(2)-law for the evaporation of spherical droplets and with theoretical predictions for the acoustic streaming velocity. We study the influence of acoustic streaming on the distribution of water vapor and temperature in the levitation device, with special attention to the vapor distribution in the emerging toroidal vortices. We also compare the evaporation rate of a droplet with and without acoustic streaming, as well as the evaporation rates in dependence of different temperatures and sound pressure levels. Finally, a simple model of protein inactivation due to heat damage is considered and studied for different evaporation settings and their respective influence on protein damage. Published by AIP Publishing.}, author = {Bänsch, Eberhard and Götz, Michael}, doi = {10.1063/1.5017936}, faupublication = {yes}, journal = {Physics of Fluids}, peerreviewed = {Yes}, title = {{Numerical} study of droplet evaporation in an acoustic levitator}, volume = {30}, year = {2018} } @article{faucris.122847604, abstract = {We present a mesh moving method within a finite element context, where the interface conditions of a two-phase flow problem are conveniently included in suitable chosen subspaces of the general trial and testfunction spaces. A weak formulation of the two-phase flow problem including species transport is derived, where the problem specific function spaces are replaced by appropriate projections operating on standard function spaces. The transfer of the variational formulation to a finite element method is straightforward and results in one set of equations for both fluidic phases. This subspace projection method is applicable to a wide range of interfacial conditions for multiphase flow problems. The method is validated for single-drop flow problems including species transfer. Furthermore, an application to the simulation of stagnant caps is presented.}, author = {Bäumler, Kathrin and Bänsch, Eberhard}, doi = {10.1016/j.jcp.2013.06.024}, faupublication = {yes}, journal = {Journal of Computational Physics}, pages = {438-457}, peerreviewed = {unknown}, title = {{A} subspace projection method for the implementation of interface conditions in a single-drop flow problem}, volume = {252}, year = {2013} } @article{faucris.121361944, abstract = {In this article we study finite element approximations of the time-dependent Stokes system on dynamically changing meshes. Applying the backward Euler method for time discretization we use the discrete Helmholtz or Stokes projection to evaluate the solution at time
We consider the popular pressure correction scheme for the solution of the time dependent Navier–Stokes equations with *traction * boundary condition. A finite element based method to improve the performance of the classical approach is proposed. The improvement is achieved by modifying the traction boundary condition for the provisional velocity in each time step. The corresponding term consists of a simple boundary functional involving the normal derivative of the pressure correction that can be evaluated in a natural and easy way in the context of finite elements.

Computational results show a significant improvement of the solution, in particular for the pressure in the case of smooth domains.

}, author = {Bänsch, Eberhard}, doi = {10.1016/j.cma.2014.06.030}, faupublication = {yes}, journal = {Computer Methods in Applied Mechanics and Engineering}, keywords = {Navier–Stokes equations; Traction boundary condition; Open boundary condition; Pressure correction; Finite elements}, pages = {198-211}, peerreviewed = {Yes}, title = {{A} finite element pressure correction scheme for the {Navier}-{Stokes} equations with traction boundary condition}, volume = {279}, year = {2014} } @article{faucris.110564124, abstract = {The photoablation process of soft tissue with free-running infrared lasers (λ = 2.70 μm, 2.79 μm, 2.94 μm) is not well understood, in particular for temperature-dependent absorption. An evaporation model has been developed, solved by the finite-element method and compared with experimental results. Both, the ablation rates and the thermal damages can be explained by a pure vaporization process with huge influence of the temperature-dependent absorption. © Springer-Verlag 1997.}, author = {Bänsch, Eberhard and Olmes, Andreas and Franke, H.-G. and Lubatschowski, Holger and Raible, M. and Dziuk, Gerhard and Ertmer, Wolfgang}, doi = {10.1007/s003400050328}, faupublication = {no}, journal = {Applied Physics B-Lasers and Optics}, note = {UnivIS-Import:2015-03-05:Pub.1997.nat.dma.lama3.modell}, pages = {659-666}, peerreviewed = {Yes}, title = {{Modelling} of {Infrared} {Soft}-{Tissue} {Photoablation} {Process}}, volume = {65}, year = {1997} } @inproceedings{faucris.117967344, address = {Bellingham}, author = {Bänsch, Eberhard and Olmes, Andreas and Brand, M. and Raible, M. and Lubatschowski, Holger and Ertmer, Wolfgang and Dziuk, Gerhard}, booktitle = {Laser-Tissue Interaction, Tissue Optics, and Laser Welding III}, doi = {10.1117/12.297904}, faupublication = {no}, note = {UnivIS-Import:2015-04-16:Pub.1998.nat.dma.lama3.modeli}, pages = {208-219}, peerreviewed = {unknown}, publisher = {SPIE-The International Society for Optical Engineering}, series = {Proc. of SPIE}, title = {{Modeling} and {Numerical} {Simulation} of the {Infrared} {Photoablation} {Process}}, volume = {3195}, year = {1998} } @article{faucris.107960424, author = {Schneider, Cornelia and Vybíral, Jan}, doi = {10.1155/2012/281085}, faupublication = {yes}, journal = {Journal of Function Spaces and Applications}, pages = {Art. ID 281085, 17}, peerreviewed = {Yes}, title = {{Homogeneity} property of {Besov} and {Triebel}-{Lizorkin} spaces}, year = {2012} } @article{faucris.115505984, abstract = {We present an adaptive finite element method for solving elliptic problems in exterior domains, that is for problems in the exterior of a bounded closed domain in ℝpartition problem based on a level set formulation. Starting from the

piecewise Mumford-Shah model for image segmentation, we follow a

method proposed by Chan and Vese, which is able to detect exterior and

interior boundaries as well as objects, whose boundaries are not

necessarily defined by gradients. The algorithm stops automatically on

the object's boundary; quantities like volumes of the different

segments or of the interface between the segments could easily be

measured. Using adaptive methods, the computational effort could be

reduced in order to efficiently segment images in two and three

spatial dimensions. We present various numerical experiments for

synthetical and real images in two and three dimensions and compare

different adaptive approaches and initial interfaces.}, author = {Fried, Michael}, faupublication = {no}, peerreviewed = {automatic}, title = {{Image} segmentation using adaptive finite elements.}, year = {2003} } @incollection{faucris.114281244, abstract = {

Dendritic growth is a nonlinear process, which falls into the category of self-organizing pattern formation phenomena. It is of great practical importance, since it appears frequently and, in the case of alloys, affects the engineering properties of the resulting solid.

In the first part of this article we report on an analysis of spatially semi-discrete approximations to the Stefan problem for two-dimensional, pure dendrites. A priori error estimates for the temperature field, the parametrization of the free boundary, relevant geometric and measuring quantities are presented and discussed. The second part describes a new algorithm for the two dimensional Stefan problem. Here the free boundary is represented as a level set. This allows to handle topological changes of the free boundary. The accuracy of the method is verified and various numerical simulations, including topological changes of the free boundary, are presented.

}, address = {Berlin, Heidelberg}, author = {Fried, Michael and Veeser, Andreas}, booktitle = {Ergodic Theory, Analysis, and Efficient Simulation of Dynamical Systems}, doi = {10.1007/978-3-642-56589-2_10}, editor = {Bernold Fiedler}, faupublication = {no}, isbn = {978-3-642-56589-2}, pages = {225 - 252}, peerreviewed = {unknown}, publisher = {Springer Berlin Heidelberg}, title = {{Simulation} and {Numerical} {Analysis} of {Dendritic} {Growth}}, year = {2001} } @book{faucris.112331164, address = {Weinheim}, author = {Fried, Michael}, edition = {2. erweiterte Auflage}, faupublication = {yes}, keywords = {Ingenieurmathematik}, peerreviewed = {unknown}, publisher = {Wiley-VCH Verlag GmbH & Co. KGaA}, series = {Für Dummies}, title = {{Mathematik} für {Ingenieure} {I} für {Dummies}}, year = {2014} } @article{faucris.108596224, author = {Schneider, Cornelia and Vybíral, Jan}, doi = {10.7169/facm/1261157806}, faupublication = {no}, journal = {Functiones et Approximatio, Commentarii Mathematici}, pages = {139--162}, peerreviewed = {Yes}, title = {{On} dilation operators in {Triebel}-{Lizorkin} spaces}, volume = {41}, year = {2009} } @article{faucris.201552267, abstract = {In this paper, we derive mathematical models for the dynamics of superparamagnetic nanoparticles under the influence of applied magnetic fields. Such models are needed in many applications, e.g. magnetic drug targeting in cancer therapy. They are the starting point for the development of stable numerical approaches and for the formulation of optimization problems, which are needed for the optimal design of magnetic field configurations. Furthermore, we show the existence and uniqueness of classical radially symmetrical solutions and illustrate their qualitative behaviour by numerical simulations using Matlab.

systems, where the transfer of a solute between a

dispersed and a continuous phase is considered, reliable

predictions of mass transfer coefficients and retention

times are indispensable. Especially in the case, where

interfacial instabilities like drop deformation and

Marangoni-convection occur, th

e influencing factors and

their quantitative nature are not yet fully understood.

In our numerical model we consider a Newtonian viscous

two phase flow, representing a single deformable drop.

Simulations are performed using the academic code

NAVIER, which features a sharp interface model and a

variational formulation of the curvature. This approach

provides an effective method for a consistent, very exact

description of discrete surface stresses.

Results of drop rise velocitie

s and mass transfer rates in

the 2D case of spherical as well as deformable drops are

presented (diameters varying from 1

mm

to 5

mm)

.

The simulations are compared to experimental results in

the system water/toluene and to numerical results of non-

deformable drops obtained by STAR-CD. Especially with

the onset of drop deformation,

the system is excellently

reflected by the simulations, i.e. the terminal velocities

calculated with NAVIER show a deviation of no more

than 4% to the experimental results.

}, author = {Bäumler, Kathrin and Wegener, Mirco and Bänsch, Eberhard and Paschedag, Anja}, booktitle = {Proceedings of the Seventh International Conference on CFD in the Minerals and Process Industries, CSIRO}, date = {2009-12-09/2009-12-11}, faupublication = {yes}, peerreviewed = {unknown}, title = {2d simulations of interfacial instabilities at deformable single doplets}, venue = {Melbourne}, year = {2009} } @incollection{faucris.121816464, abstract = {We consider optimal control-based boundary feedback stabilization of flow problems for incompressible fluids. We follow an analytical approach laid out during the last years in a series of papers by Barbu, Lasiecka, Triggiani, Raymond, and others. They have shown that it is possible to stabilize perturbed flows described by Navier-Stokes equations by designing a stabilizing controller based on a corresponding linear-quadratic optimal control problem. For this purpose, algorithmic advances in solving the associated algebraic Riccati equations are needed and investigated here. The computational complexity of the new algorithms is essentially proportional to the simulation of the forward problem.}, address = {Basel}, author = {Bänsch, Eberhard and Benner, Peter}, booktitle = {Constrained Optimization and Optimal Control for Partial Differential Equations}, doi = {10.1007/978-3-0348-0133-1_1}, editor = {Günter Leugering, Sebastian Engell, Andreas Griewank, Michael Hinze, Rolf Rannacher, Volker Schulz, Michael Ulbrich, Stefan Ulbrich,}, faupublication = {yes}, isbn = {978-3-0348-0132-4}, keywords = {Flow control; feedback; Navier-Stokes equations; Riccati equation}, pages = {5-20}, peerreviewed = {unknown}, publisher = {Birkhäuser/ Springer Basel AG}, series = {International Series of Numerical Mathematics}, title = {{Stabilization} of incompressible flow problems by {Riccati}-based feedback}, volume = {160}, year = {2012} } @inproceedings{faucris.109439484, author = {Neuß, Nicolas}, booktitle = {Proceedings of the CISC 2002}, doi = {10.1007/978-3-642-19014-8_11}, faupublication = {no}, peerreviewed = {unknown}, publisher = {Springer-Verlag}, title = {{On} using {Common} {Lisp} in scientific computing}, year = {2003} } @article{faucris.106933024, abstract = {

Based on the local discontinuous Galerkin method, two substantially different mixed formulations for the subjective surfaces problem are compared using a number of numerical tests of various types. The work also performs the energy stability analysis for both schemes.},
author = {Fried, Michael and Aizinger, Vadym and Bungert, Leon},
doi = {10.1007/s00791-018-0291-4},
faupublication = {yes},
journal = {Computing and Visualization in Science},
keywords = {Local discontinuous Galerkin method; Image segmentation; Subjective surfaces; Stability analysis; Mixed formulation; Divergence form; Edge detection},
peerreviewed = {Yes},
title = {{Comparison} of two local discontinuous {Galerkin} formulations for the subjective surfaces problem},
url = {https://link.springer.com/article/10.1007%2Fs00791-018-0291-4},
year = {2018}
}
@article{faucris.109590184,
author = {Bänsch, Eberhard and Benner, Peter and Saak, Jens and Weichelt, Heiko K.},
doi = {10.1137/140980016},
faupublication = {yes},
journal = {SIAM Journal on Scientific Computing},
pages = {832-858},
peerreviewed = {Yes},
title = {{Riccati}-based boundary feedback stabilization of incompressible {Navier}-{Stokes} flows},
volume = {37},
year = {2014}
}
@article{faucris.111245684,
abstract = {We study both, by experimental and numerical means the fluid dynamical phenomenon of edge tones. Of particular interest is the verification of scaling laws relating the frequency f to given quantities, namely d, the height of the jet, w, the stand-off distance and the velocity of the jet. We conclude that the Strouhal number S^{n} with n ≈ 1, in contrast to some analytical treatments of the problem. The constant C of the experiment agrees within 13-15% with the result of the numerical treatment. Only a weak dependence on the Reynolds number with respect to d is observed. In general, a very good agreement of the experimental and the numerical simulations is found. © 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.},
author = {Bamberger, Andreas and Bänsch, Eberhard and Siebert, Kunibert G.},
doi = {10.1002/zamm.200310122},
faupublication = {no},
journal = {ZAMM - Zeitschrift für angewandte Mathematik und Mechanik},
keywords = {Adaptive finite elements; Edge tones; Experimental investigation; Navier-stokes equations; Numerical methods},
note = {UnivIS-Import:2015-03-09:Pub.2004.nat.dma.lama3.experi},
pages = {632-646},
peerreviewed = {Yes},
title = {{Experimental} and {Numerical} {Investigation} of {Edge} {Tones}},
volume = {84},
year = {2004}
}
@article{faucris.122669624,
author = {Schneider, Cornelia and Neves, Júlio S. and Moura, Susana D.},
doi = {10.1016/j.jat.2014.07.010},
faupublication = {yes},
journal = {Journal of Approximation Theory},
pages = {82--117},
peerreviewed = {Yes},
title = {{Spaces} of generalized smoothness in the critical case: optimal embeddings, continuity envelopes and approximation numbers},
volume = {187},
year = {2014}
}
@article{faucris.117292384,
abstract = {Flow and thermal properties associated with semiconductor melt flow in an axisymmetric crucible container are studied numerically. Axisymmetric and three-dimensional computational solutions are obtained using a standard-Galerkin, finite-element solver. The crucible and crystal are optionally rotated, and the influence of gravity (through buoyancy) is accounted for via a Boussinesq approximation in the controlling Navier–Stokes equations. The results indicate a strong dependence of the flow on both rotation and buoyancy. Results for axisymmetric flows, computed with both flat and curved geometries, are presented first, and strongly suggest that rotation of crystal and crucible in the same direction (iso-rotation) is most favourable for producing a desired convexity for the crystal/melt interface. Three-dimensional results are then presented for higher Reynolds numbers, and, in particular, reveal that for iso-rotation under moderate buoyancy, the flow undergoes a switch from a steady 2D state to an unsteady 3D state, and that the temperature becomes non-trivially advected by the flow beneath the crystal. Further evidence reveals however, that on a time scale more appropriate to the crystal growth process, the (time-averaged) flow has a weaker three-dimensionality, in relation to the mean axisymmetric part, and there is only slight distortion to the temperature field beneath the crystal. A detailed examination of the instability properties is also made, revealing the underlying nonlinear mode interaction and associated frequency responses around the bifurcation point.},
author = {Bänsch, Eberhard and Davis, Dominic and Langmach, Hartmut and Reinhardt, Gerd and Uhle, Maria E.},
doi = {10.1016/j.compfluid.2005.01.004},
faupublication = {yes},
journal = {Computers & Fluids},
pages = {1400-1419},
peerreviewed = {Yes},
title = {{Two}- and three-dimensional transient melt-flow simulation in vapour-pressure-controlled {Czochralski} crystal growth},
volume = {35},
year = {2006}
}
@article{faucris.115506864,
abstract = {In this article a numerical method for the efficient simulation of instationary, viscous,incompressible flows in 2d and 3d is described. The time-discretization is based on the fractional step θ-scheme in a variant as an operator splitting, which was introduced in [3]},
author = {Bänsch, Eberhard},
faupublication = {no},
journal = {Acta Mathematica Universitatis Comenianae},
note = {UnivIS-Import:2015-03-05:Pub.1998.nat.dma.lama3.simula},
pages = {101-114},
peerreviewed = {unknown},
title = {{Simulation} of {Instationary}, {Incompressible} {Flows}},
url = {http://www.emis.de/journals/AMUC/_vol-67/_no_1/_baensch/baensch.html},
volume = {67},
year = {1998}
}
@article{faucris.123520804,
author = {Scurtu, Nicoleta and Bänsch, Eberhard},
faupublication = {yes},
journal = {Asia-Pacific Journal of Chemical Engineering},
pages = {657-673},
peerreviewed = {unknown},
title = {{Influence} of the {Weissenberg} number on the stability of {Oldroyd} kind fluids},
volume = {5},
year = {2010}
}
@incollection{faucris.112241624,
abstract = {The assessment of hemodynamics based on medical image data represents an attractive means in order to enhance diagnostic imaging capabilities, to evaluate clinical outcomes of therapies focusing on the patient's vascular system, as well as to guide minimally invasive interventional procedures in the catheter lab. We present a first evaluation along with comparisons of algorithmic approaches towards the quantitative determination of blood flow based on 2D angiography image data. © Springer-Verlag Berlin Heidelberg 2012.},
address = {Berlin, Heidelberg},
author = {Alassi, Sepideh and Kowarschik, Markus and Pohl, Thomas and Köstler, Harald and Rüde, Ulrich},
booktitle = {Bildverarbeitung für die Medizin 2012},
doi = {10.1007/978-3-642-28502-8-66},
faupublication = {yes},
isbn = {978-3-642-28502-8},
note = {UnivIS-Import:2015-10-26:Pub.2012.tech.IMMD.lsinfs.estima},
pages = {380-385},
peerreviewed = {Yes},
publisher = {Springer},
title = {{Estimating} {Blood} {Flow} {Based} on {2D} {Angiographic} {Image} {Sequences}},
url = {http://link.springer.com/content/pdf/10.1007/978-3-642-28502-8_66.pdf},
year = {2012}
}
@article{faucris.117795524,
abstract = {In this work we present and analyze a reliable and robust approximation scheme for biochemically reacting transport in the subsurface following Monod type kinetics. Water flow is modeled by the Richards equation. The proposed scheme is based on higher order finite element methods for the spatial discretization and the two step backward differentiation formula for the temporal one. The resulting nonlinear algebraic systems of equations are solved by a damped version of Newton's method. For the linear problems of the Newton iteration Krylov space methods are used. In computational experiments conducted for realistic subsurface (groundwater) contamination scenarios we show that the higher order approximation scheme significantly reduces the amount of inherent numerical diffusion compared to lower order ones. Thereby an artificial transverse mixing of the species leading to a strong overestimation of the biodegradation process is avoided. Finally, we present a robust adaptive time stepping technique for the coupled flow and transport problem which allows efficient long-term predictions of biodegradation processes. © Springer-Verlag 2004.},
author = {Bause, Markus and Knabner, Peter},
doi = {10.1007/s00791-004-0139-y},
faupublication = {yes},
journal = {Computing and Visualization in Science},
pages = {61-78},
peerreviewed = {unknown},
title = {{Numerical} simulation of contaminant biodegradation by higher order methods and adaptive time stepping},
volume = {7},
year = {2004}
}
@article{faucris.122716704,
author = {Krahl, Rolf and Bänsch, Eberhard},
doi = {10.1088/0169-5983/44/3/031409},
faupublication = {yes},
journal = {Fluid Dynamics Research},
pages = {0314019},
peerreviewed = {Yes},
title = {{On} the stability of an evaporating liquid surface},
volume = {44},
year = {2012}
}
@article{faucris.110982124,
abstract = {Drug release from collagen matrices is in most cases governed by diffusion from swollen matrices but also enzymatic matrix degradation or hydrophobic drug/ collagen interactions may contribute. To reduce water uptake and to prolong the release, insoluble collagen matrices have been chemically or dehydrothermally cross-linked. Assuming Fickian diffusion a one-dimensional model was developed and tested that allows description of water penetration, swelling and drug release and that may be expanded considering a subsequent erosion process or interactions. Swelling is described by a volume balance. For dry collagen matrices crosslinked by thermal treatment the existence of a moving front separating the polymer from a gel phase was considered, and a convective term induced by the volume expansion was incorporated. The resulting moving boundary problem was solved using a method based on biquadratic finite elements in both space and time that is stable, shows high accuracy, and is suitable for solving problems with a singularity at the initial time point. The model was verified for insoluble collagen matrices at different crosslinking degrees for both chemical and thermal treatment. For constant diffusion coefficients a close form of the solution was derived yielding equivalent results to the numerical approach. © 2002 Wiley-Liss, Inc.},
author = {Radu, Adrian Florin and Bause, Markus and Knabner, Peter and Lee, Geoffrey and Friess, Wolfgang},
doi = {10.1002/jps.10098},
faupublication = {yes},
journal = {Journal of Pharmaceutical Sciences},
keywords = {Collagen matrices; Drug release; Finite element method; Moving boundary; Numerical simulation},
note = {UnivIS-Import:2015-03-09:Pub.2002.nat.dchph.lphte.modeli},
pages = {964-972},
peerreviewed = {Yes},
title = {{Modeling} of {Drug} {Release} {From} {Collagen} {Matrices}},
volume = {91},
year = {2002}
}
@article{faucris.107977144,
author = {Neuß, Nicolas and Eberhard, Jens and Attinger, Sabine},
doi = {10.1007/s00791-002-0088-2},
faupublication = {no},
journal = {Computing and Visualization in Science},
pages = {67--72},
peerreviewed = {Yes},
title = {{Filtering} procedures for flow in heterogeneous porous media: numerical results},
volume = {5},
year = {2002}
}
@article{faucris.107402064,
author = {Neuß, Nicolas},
doi = {10.1007/978-3-642-60185-9_19},
faupublication = {no},
journal = {Computing},
pages = {19--36},
peerreviewed = {Yes},
title = {{A} new sparse matrix storage method for adaptive solving of large systems of reaction-diffusion-transport equations},
volume = {68,1},
year = {2002}
}
@article{faucris.204227413,
abstract = {This work is devoted to a posteriori error analysis of fully discrete finite element approximations to the time dependent Stokes system. The space discretization is based on popular stable spaces, including Crouzeix-Raviart and Taylor-Hood finite element methods. Implicit Euler is applied for the time discretization. The finite element spaces are allowed to change with time steps and the projection steps include alternatives that is hoped to cope with possible numerical artifices and the loss of the discrete incompressibility of the schemes. The final estimates are of optimal order in L-infinity(L-2) for the velocity error.},
author = {Bänsch, Eberhard and Karakatsani, F. and Makridakis, Charalambos},
doi = {10.1007/s10092-018-0259-2},
faupublication = {yes},
journal = {Calcolo},
keywords = {A posteriori error estimators;Time dependent Stokes;Reconstruction;Adaptivity;Mesh change;Crouzeix-Raviart element},
peerreviewed = {Yes},
title = {{A} posteriori error estimates for fully discrete schemes for the time dependent {Stokes} problem},
volume = {55},
year = {2018}
}
@article{faucris.117284244,
abstract = {We present the topology optimization of an assembly consisting of a piezoelectric layer attached to a plate with support. The optimization domain is the piezoelectric layer. Using the SIMP (Solid Isotropic Material with Penalization) method with forced vibrations by harmonic electrical excitation, we achieve a maximization of the dynamic displacement. We show that the considered objective function can be used under certain boundary conditions to optimize the sound radiation. The vibrational patterns resulting from the optimization are analysed in comparison with the modes from an eigenvalue analysis. Multiple-frequency optimization is achieved by adaptive weighted sums. As a second optimization criterion, a flat frequency response is integrated in the optimization process. },
author = {Wein, Fabian and Kaltenbacher, Manfred and Leugering, Günter and Bänsch, Eberhard and Schury, Fabian},
doi = {10.3233/JAE-2009-1022},
faupublication = {yes},
journal = {International Journal of Applied Electromagnetics and Mechanics},
keywords = {Topology optimization; piezoelectric coupling; sound radiation},
month = {Jan},
pages = {201-221},
peerreviewed = {Yes},
title = {{Topology} optimization of a piezoelectric-mechanical actuator with single- and multiple-frequency excitation},
url = {http://content.iospress.com/articles/international-journal-of-applied-electromagnetics-and-mechanics/jae01022},
volume = {30},
year = {2009}
}
@inproceedings{faucris.120426724,
address = {Basel},
author = {Bänsch, Eberhard and Morin, Pedro and Nochetto, Ricardo},
booktitle = {Free Boundary Problems: Theory and Applications},
faupublication = {no},
isbn = {3-7643-2193-8},
note = {UnivIS-Import:2015-04-16:Pub.2004.nat.dma.lama3.finite_7},
pages = {53-63},
publisher = {Birkhäuser},
series = {Int. Series of Num. Math.},
title = {{Finite} {Element} {Methods} for {Surface} {Diffusion}},
venue = {Trento},
volume = {147},
year = {2004}
}
@article{faucris.122858384,
abstract = {

Deeper investigation of time discretization for free surface problems is a widely neglected problem. Many existing approaches use an explicit decoupling which is only conditionally stable. Only few unconditionally stable methods are known, and known methods may suffer from too strong numerical dissipativity. They are also usually of first rder only [1, 9]. We are therefore looking for unconditionally stable, minimally dissipative methods of higher order.

Linearly implicit Runge-Kutta (LIRK) methods are a class of one-step methods that require the solution of linear systems in each time step of a nonlinear system. They are well suited for discretized PDEs, e.g. parabolic problems [7]. They have been used successfully to solve the incompressible Navier-Stokes equations [5]. We suggest an adaption of these methods for free surface problems and compare different approximations to the Jacobian matrix needed for such methods. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

}, author = {Bänsch, Eberhard and Weller, Stephan}, doi = {10.1002/pamm.201210251}, faupublication = {yes}, journal = {Proceedings in Applied Mathematics and Mechanics}, pages = {525-526}, peerreviewed = {Yes}, title = {{Linearly} implicit time discretization for free surface problems}, volume = {12}, year = {2012} } @article{faucris.111252064, abstract = {An adaptive finite element method is developed for a class of free or moving boundary problems modeling island dynamics in epitaxial growth. Such problems consist of an adatom (adsorbed atom) diffusion equation on terraces of different height; boundary conditions on terrace boundaries including the kinetic asymmetry in the adatom attachment and detachment; and the normal velocity law for the motion of such boundaries determined by a two-sided flux, together with the one-dimensional "surface" diffusion. The problem is solved using two independent meshes: a two-dimensional mesh for the adatom diffusion and a one-dimensional mesh for the boundary evolution. The diffusion equation is discretized by the first-order implicit scheme in time and the linear finite element method in space. A technique of extension is used to avoid the complexity in the spatial discretization near boundaries. All the elements are marked, and the marking is updated in each time step, to trace the terrace height. The evolution of the terrace boundaries includes both the mean curvature flow and the surface diffusion. Its governing equation is solved by a semi-implicit front-tracking method using parametric finite elements. Simple adaptive techniques are employed in solving the adatom diffusion as well as the boundary motion problem. Numerical tests on pure geometrical motion, mass balance, and the stability of a growing circular island demonstrate that the method is stable, efficient, and accurate enough to simulate the growing of epitaxial islands over a sufficiently long time period. © 2003 Elsevier Inc. All rights reserved.}, author = {Bänsch, Eberhard and Haußer, Frank and Lakkis, Omar and Li, Bo and Voigt, Axel}, doi = {10.1016/j.jcp.2003.09.029}, faupublication = {no}, journal = {Journal of Computational Physics}, keywords = {Adaptivity; Adatom diffusion; Attachment-detachment kinetics; Epitaxial growth; Finite elements; Free or moving boundary problem; Front tracking; Island dynamics; Mean curvature flow; Surface diffusion}, note = {UnivIS-Import:2015-03-09:Pub.2004.nat.dma.lama3.finite}, pages = {409-434}, peerreviewed = {Yes}, title = {{Finite} {Element} {Method} for {Epitaxial} {Growth} with {Attachment}-{Detachment} {Kinetics}}, volume = {194}, year = {2004} } @article{faucris.200176305, abstract = {A large portion of terrestrially derived carbon outgasses as carbon dioxide (CO2) from streams and rivers to the atmosphere. Particularly, the amount of CO2 outgassing from small headwater streams is highly uncertain. Conservative estimates suggest that they contribute 36 % (i.e. 0.93 petagrams (Pg) C yr−1) of total CO2 outgassing from all fluvial ecosystems on the globe. In this study, stream

2, where Re is the Reynolds number and ε the thinness of the cone-plate gap. We establish this fact by means of rigorous energy estimates and numerical simulations. Surprisingly enough, this approximation is valid though the primary flow is not itself a solution of the Navier-Stokes equations, and it does not even fulfill the correct boundary conditions, which are in this particular case discontinuous along a line, thus not allowing for a usual Leray solution. To overcome this difficulty we construct a suitable corrector.}, author = {Azerad, Pascal and Bänsch, Eberhard}, doi = {10.1007/s00021-003-0093-3}, faupublication = {no}, journal = {Journal of Mathematical Fluid Mechanics}, keywords = {Asymptotic analysis; CFD; Finite elements; Flow chamber; Haemodynamics; Haemostasis; Navier-Stokes equations; Nonlinear stability; Rheometry; Rotating fluids; Shallow domains}, note = {UnivIS-Import:2015-03-09:Pub.2004.nat.dma.lama3.quasis}, pages = {253-271}, peerreviewed = {Yes}, title = {{Quasi}-{Stability} of the {Primary} {Flow} in a {Cone} and {Plate} {Viscometer}}, volume = {6}, year = {2004} } @incollection{faucris.118371704, abstract = {Single crystals of Cadmium-Zinc-Telluride are used as a substrate material for the production of infrared detectors and are usually grown by the vertical Bridgman method. We present a simulation of the whole growth process in two steps: In the first step, the (stationary) heat transport in the furnace is modeled and calculated for different positions of the ampoule. This provides information about the most important parameter during this process: the temperature distribution in furnace and ampoule. The obtained temperatures are then used in the second step as boundary conditions for the (time dependent) simulation of temperature and convection in the ampoule. Only the use of adaptive finite element methods allows an efficient numerical simulation of the moving phase boundary, the convection in the melt and the temperature distribution in melt and crystal. Numerical results are presented for both furnace and ampoule simulations.}, address = {Berlin}, author = {Boschert, Stefan and Schmidt, Alfred and Siebert, Kunibert G. and Bänsch, Eberhard and Benz, Klaus-Werner and Dziuk, Gerhard and Kaiser, Thomas}, booktitle = {Mathematics - Key Technology for the Future}, doi = {10.1007/978-3-642-55753-8_26}, editor = {Willi Jäger, Hans-Joachim Krebs}, faupublication = {no}, isbn = {3-540-44220-0}, note = {UnivIS-Import:2015-04-20:Pub.2003.nat.dma.lama3.simula}, pages = {331-342}, peerreviewed = {unknown}, publisher = {Springer}, title = {{Simulation} of {Industrial} {Crystal} {Growth} by the {Vertical} {Bridgman} {Method}}, year = {2003} } @incollection{faucris.118885844, address = {Berlin}, author = {Bänsch, Eberhard and Höhn, Burkhard}, booktitle = {Scientific Computing in Chemical Engineering II}, editor = {Keil, F., Mackens, W., Voß, H., Werther, J.}, faupublication = {no}, isbn = {3-540-65848-3}, note = {UnivIS-Import:2015-04-20:Pub.1999.nat.dma.lama3.numeri}, pages = {328-335}, peerreviewed = {unknown}, publisher = {Springer}, title = {{Numerical} {Simulation} of a {Silicon} {Floating} {Zone} with a {Free} {Capillary} {Surface}}, volume = {1}, year = {1999} } @article{faucris.111241064, abstract = {Axisymmetric and 3D calculations of melt flow have been performed for a configuration used at the vapour-pressure-controlled Czochalski growth of GaAs single crystals. Thermal boundary conditions were adapted from a global simulation of the temperature field. The axisymmetric calculations with the code NAVIER confirmed the ones previously perfomed with FIDAP™. The 3D calculations showed that the flow exhibits an asymmetric transient behaviour beyond a certain critical Reynolds number. © 2004 Elsevier B.V. All rights reserved.}, author = {Bänsch, Eberhard and Davis, Dominic and Langmach, Hartmut and Miller, Wolfram and et al.}, author_hint = {Bänsch Eberhard, Davis Dominic, Langmach Hartmut, Miller Wolfram, Rehse Uwe, Reinhardt Gerd, Uhle Manfred}, doi = {10.1016/j.jcrysgro.2004.02.030}, faupublication = {no}, journal = {Journal of Crystal Growth}, keywords = {A1. Computer simulation; A1. Convection; A1. Heat transfer; A2. Liquid encapsulated Czochralski method}, note = {UnivIS-Import:2015-03-09:Pub.2004.nat.dma.lama3.axisym}, pages = {60-66}, peerreviewed = {Yes}, support_note = {Author relations incomplete. You may find additional data in field 'author_hint'}, title = {{Axisymmetric} and {3D} {Calculations} of {Melt} {Flow} {During} {VCz} {Growth}}, volume = {266}, year = {2004} } @article{faucris.122616824, abstract = {In this paper we show first-order convergence of a multi-point flux approximation control volume method (MPFA) on unstructured triangular grids. In this approach the flux approximation is derived directly in the physical space. In order to do this, we introduce a perturbed mixed finite element method that is equivalent to the MPFA scheme and prove the first-order convergence of this approach. Moreover, we carefully compare the computational performance properties of the MPFA method with those of a lowest order Raviart-Thomas and Brezzi-Douglas-Marini mixed finite element approximation. © 2010 Springer-Verlag.}, author = {Bause, Markus and Hoffmann, Joachim and Knabner, Peter}, doi = {10.1007/s00211-010-0290-y}, faupublication = {yes}, journal = {Numerische Mathematik}, pages = {1-29}, peerreviewed = {Yes}, title = {{First}-order convergence of multi-point flux approximation on triangular grids and comparison with mixed finite element methods}, volume = {116}, year = {2010} } @article{faucris.117254764, abstract = {

We derive residual-based a posteriori error estimates of optimal order for fully discrete approximations for linear parabolic problems. The time discretization uses the Crank--Nicolson method, and the space discretization uses finite element spaces that are allowed to change in time. The main tool in our analysis is the comparison with an appropriate reconstruction of the discrete solution, which is introduced in the present paper.

Read More: http://epubs.siam.org/doi/abs/10.1137/110839424

Read More: http://epubs.siam.org/doi/abs/10.1137/110839424

}, author = {Bänsch, Eberhard and Karakatsani, F. and Makridakis, Charalambos}, doi = {10.1137/110839424}, faupublication = {yes}, journal = {SIAM Journal on Numerical Analysis}, pages = {2845-2872}, peerreviewed = {Yes}, title = {{A} posteriori error control for fully discrete {Crank}-{Nicolson} schemes}, volume = {50}, year = {2012} } @incollection{faucris.117290844, abstract = {

The study of fluid flow inside compliant vessels, which are deformed under an action of the fluid, is important due to many biochemical and biomedical applications, e.g. the flows in blood vessels.

The mathematical problem consists of the 3D Navier-Stokes equations for incompressible fluids coupled with the differential equations, which describe the displacements of the vessel wall (or elastic structure). We study the fluid flow in a tube with different types of boundaries: inflow boundary, outflow boundary and elastic wall and prescribe different boundary conditions of Dirichlet- and Neumann types on these boundaries. The velocity of the fluid on the elastic wall is given by the deformation velocity of the wall.

In this publication we present the mathematical modelling for the elastic structures based on the shell theory, the simplifications for cylinder-type shells, the simplifications for arbitrary shells under special assumptions, the mathematical model of the coupled problem and some numerical results for the pressure-drop problem with cylindrical elastic structure.

}, author = {Bänsch, Eberhard and Goncharova, Olga and Koop, Andreas and Kröner, Dietmar}, booktitle = {Computational Science and High Performance Computing III}, doi = {10.1007/978-3-540-69010-8_9}, editor = {Egon Krause, Yurii I. Shokin, Michael Resch, Nina Shokina}, faupublication = {yes}, pages = {102-121}, peerreviewed = {unknown}, publisher = {Springer}, series = {Notes on Numerical Fluid Mechanics and Multidisciplinary Design}, title = {{Mathematical} and numerical modelling of fluid flow in elastic tubes}, volume = {101}, year = {2008} } @incollection{faucris.118854164, address = {Southampton}, author = {Bänsch, Eberhard}, booktitle = {Adaptive Finite and Boundary Element Methods}, faupublication = {no}, note = {UnivIS-Import:2015-04-20:Pub.1993.nat.dma.lama3.adapti}, pages = {47-76}, peerreviewed = {unknown}, publisher = {Computational Mechanics Publications}, title = {{Adaptive} {Finite}-{Element} {Techniques} for {Navier}-{Stokes} {Equations} and other {Transient} {Problems}}, year = {1993} } @article{faucris.107401184, abstract = {We consider the laminar viscous channel flow over a porous surface. The size of the pores is much smaller than the size of the channel and it is important to determine the effective boundary conditions at the porous surface. We study the corresponding boundary layers, and, by a rigorous asymptotic expansion, we obtain Saffman's modification of the interface condition observed by Beavers and Joseph. The effective coefficient in the law is determined through an auxiliary boundary-layer type problem, whose computational and modeling aspects are discussed in detail. Furthermore, the approximation errors for the velocity and for the effective mass flow are given as powers of the characteristic pore size $\eps$. Finally, we give the interface condition linking the effective pressure fields in the porous medium and in the channel, and determine the jump of the effective pressures explicitly.}, author = {Jäger, Willi and Mikelic, Andro and Neuß, Nicolas}, doi = {10.1137/S1064827599360339}, faupublication = {no}, journal = {SIAM Journal on Computing}, keywords = {Homogenization; periodic structures; Navier-Stokes; Beavers-Joseph; interface law; boundary layer; unbounded domain; finite elements; multigrid;}, pages = {2006--2028}, peerreviewed = {Yes}, title = {{Asymptotic} analysis of the laminar viscous flow over a porous bed}, volume = {22,6}, year = {2001} } @misc{faucris.116891104, author = {Bänsch, Eberhard}, faupublication = {no}, peerreviewed = {automatic}, title = {{Numerical} methods for the instationary {Navier}-{Stokes} equations with a free capillary surface}, year = {1998} } @article{faucris.123375384, author = {Schneider, Cornelia}, doi = {10.4171/ZAA/1409}, faupublication = {no}, journal = {Zeitschrift für Analysis und ihre Anwendungen}, pages = {275--302}, peerreviewed = {Yes}, title = {{Trace} operators in {Besov} and {Triebel}-{Lizorkin} spaces}, volume = {29}, year = {2010} } @article{faucris.106601924, abstract = {
A novel finite element method for the 3d simulation of (many) particles in a Newtonian carrier liquid is presented. The methods features the celebrated one domain approach, a *subspace projection method* to account for the rigid body motion within the particles and operator splitting. Combined with local mesh refinement the method results in a fast and accurate, though conceptually simple to implement algorithm.

Validation is achieved using the sedimentation of one particle and comparing the resulting drag coefficient with theoretical and experimental results. Furthermore, a viscometer is considered, where the effective viscosity of a particle laden fluid is compared with analytic results.

}, author = {Prignitz, Rodolphe and Bänsch, Eberhard}, doi = {10.1016/j.jcp.2013.12.030}, faupublication = {yes}, journal = {Journal of Computational Physics}, pages = {249-272}, peerreviewed = {Yes}, title = {{Particulate} flows with the subspace projection method}, volume = {260}, year = {2014} } @article{faucris.122672704, author = {Schneider, Cornelia and Vybíral, Jan}, doi = {10.1016/j.jfa.2012.12.005}, faupublication = {yes}, journal = {Journal of Functional Analysis}, pages = {1197--1237}, peerreviewed = {Yes}, title = {{Non}-smooth atomic decompositions, traces on {Lipschitz} domains, and pointwise multipliers in function spaces}, volume = {264}, year = {2013} } @article{faucris.122619464, abstract = {We present a mass conservative finite element approach of second order accuracy for the numerical approximation of reactive solute transport in porous media modeled by a coupled system of advection-diffusion-reaction equations. The lowest order Brezzi-Douglas-Marini (BDM ) mixed finite element method is used. A modification based on the hybrid form of the approach is suggested for the discretization of the advective term. It is demonstrated numerically that this leads to optimal second order convergence of the flux variable. The modification improves the convergence behavior of the classical BDM scheme, which is known to be suboptimal of first order accuracy only for advection-diffusion problems; cf. [8]. Moreover, the new scheme shows more robustness for high Péclet numbers than the classical approach. A comparison with the Raviart-Thomas element (RT ) of second order accuracy for the approximation of the flux variable is also presented. For the case of strongly advection-dominated problems we propose a full upwind scheme. Various numerical studies, including also a nonlinear test problem, are presented to illustrate the numerical performance properties of the considered numerical methods. © 2011 Elsevier Ltd.}, author = {Brunner, Fabian and Radu, Adrian Florin and Bause, Markus and Knabner, Peter}, doi = {10.1016/j.advwatres.2011.10.001}, faupublication = {yes}, journal = {Advances in Water Resources}, keywords = {Mixed finite element methods; Optimal order convergence; Reactive transport}, pages = {163-171}, peerreviewed = {Yes}, title = {{Optimal} order convergence of a modified {BDM} 1 mixed finite element scheme for reactive transport in porous media}, volume = {35}, year = {2012} } @article{faucris.123724524, author = {Neuß, Nicolas and Neuss-Radu, Maria and Mikelic, Andro}, doi = {10.1080/00036810500340476}, faupublication = {no}, journal = {Applicable Analysis}, pages = {479-502}, peerreviewed = {Yes}, title = {{Effective} laws for the {Poisson} equation on domains with curved oscillating boundaries}, year = {2006} } @book{faucris.110558844, abstract = {The conference Challenges In Scientific Computing (CISC 2002) took place from October, 2 to 5, 2002. The hosting institution was the Weierstrass Insti tute for Applied Analysis and Stochastics (WIAS) in Berlin, Germany. The main purpose of this meeting was to draw together researchers working in the fields of numerical analysis and scientific computing with a common interest in the numerical treatment and the computational solution of systems of nonlinear partial differential equations arising from applications of physical and engineering problems. The main focus of the conference was on the problem class of non linear transport/diffusion/reaction systems, chief amongst these being: the Navier-Stokes equations, semiconductor-device equations and porous media flow problems. The emphasis was on unsolved problems, challenging open questions from applications and assessing the various numerical methods used to handle them, rather than concentrate on accurate results from "solved" problems. Thanks to the participants it was an interesting meeting. The presentations stimulated exchanging ideas and lively discussions. This proceedings comprises 13 papers form the conference, ranging from numerical methods for flow problems, multigrid methods, semiconductor and microwave simulation, solution methods, finite element analysis to software aspects. This interesting conference would not have been possible without the help of the staff of the WIAS. I thank all participants, and all our supporters, especially those not onstage, for making the conference a success.}, address = {Berlin}, editor = {Bänsch, Eberhard}, faupublication = {no}, isbn = {978-3-540-40887-1}, note = {UnivIS-Import:2015-07-08:Pub.2003.nat.dma.lama3.challe}, publisher = {Springer}, series = {Lecture Notes in Computational Science and Engineering}, title = {{Challenges} in {Scientific} {Computing} - {CISC} 2002}, url = {http://www.springer.com/dal/home/?SGWID=1-40356-22-12701795-0}, volume = {35}, year = {2003} } @article{faucris.109599424, author = {Bänsch, Eberhard and Karakatsani, F. and Makridakis, Charalambos}, doi = {10.1016/j.apnum.2011.08.008}, faupublication = {yes}, journal = {Applied Numerical Mathematics}, pages = {35-63}, peerreviewed = {Yes}, title = {{The} effect of mesh modification in time on the error control of fully discrete approximations for parabolic equations}, volume = {67}, year = {2013} } @article{faucris.107229144, abstract = {The work formulates and evaluates the local discontinuous Galerkin method for the subjective surfaces problem based on the curvature driven level set equation. A new mixed formulation simplifying the treatment of nonlinearities is proposed. The numerical algorithm is evaluated using several artificial and realistic test cases.}, author = {Bungert, Leon and Aizinger, Vadym and Fried, Michael}, doi = {10.1007/s10851-016-0695-z}, faupublication = {yes}, journal = {Journal of Mathematical Imaging and Vision}, pages = {in press}, peerreviewed = {unknown}, title = {{A} {Discontinuous} {Galerkin} {Method} for the {Subjective} {Surfaces} {Problem}}, year = {2016} } @article{faucris.107967024, author = {Schneider, Cornelia and Haroske, Dorothee D.}, doi = {10.1016/j.jat.2008.12.004}, faupublication = {no}, journal = {Journal of Approximation Theory}, pages = {723--747}, peerreviewed = {Yes}, title = {{Besov} spaces with positive smoothness on {$\{Bbb} {R}^n$}, embeddings and growth envelopes}, volume = {161}, year = {2009} } @article{faucris.204228485, abstract = {We develop a preconditioner for systems arising from space-time finite element discretizations of parabolic equations. The preconditioner is based on a transformation of the coupled system into block diagonal form and an efficient solution strategy for the arising 2 x 2 blocks. The suggested strategy makes use of an inexact factorization of the Schur complement of these blocks, for which uniform bounds on the condition number can be proven. The main computational effort of the preconditioner lies in solving implicit Euler-like problems, which allows for the usage of efficient standard solvers. Numerical experiments are performed to corroborate our theoretical findings.}, author = {Bänsch, Eberhard and Basting, Steffen}, doi = {10.1051/m2an/2016055}, faupublication = {yes}, journal = {Esaim-Mathematical Modelling and Numerical Analysis-Modelisation Mathematique Et Analyse Numerique}, keywords = {Finite element method;time discretization;discontinuous Galerkin;preconditioning.}, pages = {1173-1195}, peerreviewed = {Yes}, title = {{PRECONDITIONERS} {FOR} {THE} {DISCONTINUOUS} {GALERKIN} {TIME}-{STEPPING} {METHOD} {OF} {ARBITRARY} {ORDER}}, volume = {51}, year = {2017} } @article{faucris.117650324, abstract = {A numerical solution of the one-dimensional diffusion equation is presented to describe the 5-layer laminate technique for estimating the saturation solubility of a drug in a thin polymer film. The boundary and initial conditions encompass a donor layer, a separating membrane, and an acceptor layer. Alteration of the drug's partition coefficient between donor and separating membrane has little influence on drug accumulation with the acceptor. The diffusivity in the separating membrane should be high to promote a short experimental time to achieve saturation equilibrium in the acceptor layer. The essential parameter to give rapid equilibrium is the thickness of the acceptor polymer film. For values of diffusivity typical for drugs of molecular weight around 500 an acceptor layer thickness of 10 μm-20 μm is required to achieve equilibrium within less than 10 d. These simulations allow the selection of suitable experimental conditions to make the 5-layer laminate technique a viable method for routine use. © 2014 Informa Healthcare USA, Inc.}, author = {Bänsch, Eberhard and Lee, Geoffrey and Reismann, Simone}, doi = {10.3109/10837450.2013.819016}, faupublication = {yes}, journal = {Pharmaceutical Development and Technology}, keywords = {Diffusion equation; Polymer; Saturation solubility; Thin film; Transdermal}, note = {UnivIS-Import:2015-03-09:Pub.2014.nat.dchph.lphte.numeri}, pages = {634-640}, peerreviewed = {Yes}, title = {{Numerical} {Solution} for 5-{Layer} {Laminate} {Technique} to determine {Saturation} {Solubility} of a {Drug} in a {Thin} {Film} of {Pressure} {Sensitive} {Adhesive}}, url = {http://www.pharmtech.uni-erlangen.de}, volume = {19}, year = {2014} } @inproceedings{faucris.112056604, address = {Providence}, author = {Bänsch, Eberhard and Schmidt, Alfred}, booktitle = {Computational Crystal Growers Workshop}, faupublication = {no}, note = {UnivIS-Import:2015-04-16:Pub.1992.nat.dma.lama3.afinit}, pages = {16-20}, publisher = {American Mathematical Society}, title = {{A} {Finite} {Element} {Method} for {Dendritic} {Growth}}, year = {1992} } @article{faucris.115192924, abstract = {An algorithm for local refinement of a given conforming triangulation in 2 or 3 dimensions is presented. Proofs for the finiteness of the algorithm and stability of the obtained triangulations are given. © 1991.}, author = {Bänsch, Eberhard}, doi = {10.1016/0899-8248(91)90006-G}, faupublication = {no}, journal = {IMPACT of Computing in Science and Engineering}, note = {UnivIS-Import:2015-03-05:Pub.1991.nat.dma.lama3.localm}, pages = {181-191}, peerreviewed = {No}, title = {{Local} {Mesh} {Refinement} in 2 and 3 {Dimensions}}, volume = {3}, year = {1991} } @article{faucris.115705084, author = {Bänsch, Eberhard and Höhn, Burkhard}, doi = {10.1137/S1064827598343991}, faupublication = {no}, journal = {SIAM Journal on Scientific Computing}, note = {UnivIS-Import:2015-03-09:Pub.2000.nat.dma.lama3.numeri}, pages = {2144-2162}, peerreviewed = {Yes}, title = {{Numerical} {Treatment} of the {Navier}-{Stokes} {Equations} with {Slip} {Boudary} {Condition}}, volume = {21}, year = {2000} } @article{faucris.204231341, author = {Bänsch, Eberhard and Basting, Steffen and Fuhrmann, Eckhart and Dreyer, Michael}, doi = {10.1007/s00231-015-1600-9}, faupublication = {yes}, journal = {Heat and Mass Transfer}, pages = {855-876}, peerreviewed = {Yes}, title = {{Free} surface deformation and heat transfer by thermocapillary convection}, volume = {52}, year = {2016} } @article{faucris.120783784, abstract = {We develop preconditioners for systems arising from finite element discretizations of parabolic problems which are fourth order in space. We consider boundary conditions which yield a natural splitting of the discretized fourth order operator into two (discrete) linear second order elliptic operators, and exploit this property in designing the preconditioners. The underlying idea is that efficient methods and software to solve second order problems with optimal computational effort are widely available. We propose symmetric and non-symmetric preconditioners, along with theory and numerical experiments. They both document crucial properties of the preconditioners as well as their practical performance. It is important to note that we neither need