Local mass-corrections for continuous pressure approximations of incompressible flow

Beitrag in einer Fachzeitschrift


Details zur Publikation

Autorinnen und Autoren: Gmeiner B, Waluga C, Wohlmuth BI
Zeitschrift: SIAM Journal on Numerical Analysis
Verlag: Society for Industrial and Applied Mathematics
Jahr der Veröffentlichung: 2014
Band: 52
Heftnummer: 6
Seitenbereich: 2931-2956
ISSN: 0036-1429


Abstract

In this work, we discuss a family of finite elemen t discretizations for the incompressible Stokes problem using continuous pressure approximations on simplicial meshes. We show that after a simple and cheap correction, the mass-fluxes obtained by the considered schemes preserve local conservation on dual cells without reducing the convergence order. This allows the direct coupling to vertex-centered finite volume discretizations of transport equations. Further, we can postprocess the mass fluxes independently for each dual box to obtain an elementwise conservative velocity approximation of optimal order that can be used in cell-centered finite volume or discontinuous Galerkin schemes. Numerical examples for stable and stabilized methods are given to support our theoretical findings. Moreover, we demonstrate the coupling to vertex- and cell-centered finite volume methods for advective transport.


FAU-Autorinnen und Autoren / FAU-Herausgeberinnen und Herausgeber

Gmeiner, Björn Dr.-Ing.
Lehrstuhl für Informatik 10 (Systemsimulation)


Einrichtungen weiterer Autorinnen und Autoren

Technische Universität München (TUM)


Zitierweisen

APA:
Gmeiner, B., Waluga, C., & Wohlmuth, B.I. (2014). Local mass-corrections for continuous pressure approximations of incompressible flow. SIAM Journal on Numerical Analysis, 52(6), 2931-2956. https://dx.doi.org/10.1137/140959675

MLA:
Gmeiner, Björn, Christian Waluga, and B. I. Wohlmuth. "Local mass-corrections for continuous pressure approximations of incompressible flow." SIAM Journal on Numerical Analysis 52.6 (2014): 2931-2956.

BibTeX: 

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