Prof. Dr. Peter Knabner



Organisationseinheit


Lehrstuhl für Angewandte Mathematik (Modellierung und Numerik)


Preise / Auszeichnungen


2009 : Prize for “the most innovative method“ for the solution of the MoMaS benchmark problem on reactive problems



Projektleitung

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MPFA (Multi Point Flux Approximation) und gemischt-hybride Finite Element Methoden für Fluss und Transport in porösen Medien
Prof. Dr. Peter Knabner
(01.01.2012 - 31.12.2013)

Entwicklung neuer photokatalytischer Filtersysteme zur Luftreinigung von Nanopartikeln, organischen Zusätzen und Bakterien mit Hilfe numerischer Simulationen
Prof. Dr. Peter Knabner
(01.10.2009 - 30.09.2011)

Efficient Numerical Methods for Large Partial Differential Complementarity Systems arising in Multispecies Reactive Transport with Minerals in Porous Media
Prof. Dr. Peter Knabner; PD Dr. Serge Kräutle
(01.01.2007 - 31.12.2011)

Der Einfluss von Kolloiden auf Wasserfluss und Stofftransport in Böden: Randaspekt oder Schlüsselprozess?
Prof. Dr. Peter Knabner
(01.11.2006 - 31.12.2009)

(Identifikation, Optimierung und Steuerung für technische Anwendungen):
Identifizierung nichtlinearer Koeffizientenfunktionen des reaktiven Transports durch poröse Medien unter Verwendung rekursiver und formfreier Ansätze
Prof. Dr. Peter Knabner
(01.06.2006 - 30.04.2010)


Mitarbeit in Forschungsprojekten


IntComSin: Grenzflächen, komplexe Strukturen und singuläre Limiten in der Kontinuumsmechanik
Prof. Dr. Günther Grün
(01.04.2018 - 30.09.2022)


Publikationen (Download BibTeX)

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Schulz, R., & Knabner, P. (2017). AN EFFECTIVE MODEL FOR BIOFILM GROWTH MADE BY CHEMOTACTICAL BACTERIA IN EVOLVING POROUS MEDIA. SIAM Journal on Applied Mathematics, 77(5), 1653-1677. https://dx.doi.org/10.1137/16M108817X
Knabner, P., & Rannacher, R. (2017). A Priori Error Analysis for the Galerkin Finite Element Semi-discretization of a Parabolic System with Non-Lipschitzian Nonlinearity. Vietnam Journal of Mathematics, 45, 179-198. https://dx.doi.org/10.1007/s10013-016-0214-y
Frank, F., & Knabner, P. (2017). Convergence analysis of a BDF2/mixed finite element discretization of a Darcy–Nernst–Planck–Poisson system. Esaim-Mathematical Modelling and Numerical Analysis-Modelisation Mathematique Et Analyse Numerique, 51(5), 1883-1902. https://dx.doi.org/10.1051/m2an/2017002
Rupp, A., & Knabner, P. (2017). Convergence order estimates of the local discontinuous Galerkin method for instationary Darcy flow. Numerical Methods For Partial Differential Equations, 33(4), 1374-1394. https://dx.doi.org/10.1002/num.22150
Schulz, R., & Knabner, P. (2017). Derivation and analysis of an effective model for biofilm growth in evolving porous media. Mathematical Methods in the Applied Sciences, 40(8), 2930-2948. https://dx.doi.org/10.1002/mma.4211
Gahn, M., Neuss-Radu, M., & Knabner, P. (2017). Derivation of an Effective Model for Metabolic Processes in Living Cells Including Substrate Channeling. Vietnam Journal of Mathematics, 45, 265-293. https://dx.doi.org/10.1007/s10013-016-0227-6
Gahn, M., Neuss-Radu, M., & Knabner, P. (2017). DERIVATION OF EFFECTIVE TRANSMISSION CONDITIONS FOR DOMAINS SEPARATED BY A MEMBRANE FOR DIFFERENT SCALING OF MEMBRANE DIFFUSIVITY. Discrete and Continuous Dynamical Systems, 10(4), 773-797. https://dx.doi.org/10.3934/dcdss.2017039
Hoffmann, J., Kräutle, S., & Knabner, P. (2017). Existence and uniqueness of a global solution for reactive transport with mineral precipitation-dissolution and aquatic reactions in porous media. SIAM Journal on Mathematical Analysis, 49(6), 4812-4837. https://dx.doi.org/10.1137/16M1109266
Mahato, H.S., Kräutle, S., Böhm, M., & Knabner, P. (2017). Upscaling of a system of semilinear parabolic partial differential equations coupled with a system of nonlinear ordinary differential equations originating in the context of crystal dissolution and precipitation inside a porous medium: existence theory and periodic homogenization. Advances in Mathematical Sciences and Applications, 26(1), 39-81.
Brunner, F., Fischer, J., & Knabner, P. (2016). Analysis of a Modified Second-Order Mixed Hybrid $BDM_1$ Finite Element Method for Transport Problems in Divergence Form. SIAM Journal on Numerical Analysis, 54(4), 2359-2378. https://dx.doi.org/10.1137/15M1035379

Zuletzt aktualisiert 2016-18-06 um 04:27