Local mass-corrections for continuous pressure approximations of incompressible flow
Gmeiner B, Waluga C, Wohlmuth BI (2014)
Publication Type: Journal article
Publication year: 2014
Journal
Publisher: Society for Industrial and Applied Mathematics
Book Volume: 52
Pages Range: 2931-2956
Journal Issue: 6
URI: http://www.terraneo.fau.de/docs/gmeiner-waluga-wohlmuth-2014-mass-conservation.pdf
DOI: 10.1137/140959675
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.
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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://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.
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