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Discontinuous Galerkin subgrid finite element method for heterogeneous Brinkman’s equations. (English) Zbl 1280.76061

Lirkov, Ivan (ed.) et al., Large-scale scientific computing. 7th international conference, LSSC 2009, Sozopol, Bulgaria, June 4–8, 2009. Revised papers. Berlin: Springer (ISBN 978-3-642-12534-8/pbk). Lecture Notes in Computer Science 5910, 14-25 (2010).
Summary: We present a two-scale finite element method for solving Brinkman’s equations with piece-wise constant coefficients. This system of equations model fluid flows in highly porous, heterogeneous media with complex topology of the heterogeneities. We make use of the recently proposed discontinuous Galerkin FEM for Stokes equations by J. Wang and X. Ye in [SIAM J. Numer. Anal. 45, No. 3, 1269–1286 (2007; Zbl 1138.76049)] and the concept of subgrid approximation developed for Darcy’s equations by T. Arbogast in [SIAM J. Numer. Anal. 42, No. 2, 576–598 (2004; Zbl 1078.65092)]. In order to reduce the error along the coarse-grid interfaces we have added a alternating Schwarz iteration using patches around the coarse-grid boundaries. We have implemented the subgrid method using Deal.II FEM library, and we present the computational results for a number of model problems.
For the entire collection see [Zbl 1204.65003].

MSC:

76S05 Flows in porous media; filtration; seepage
76M10 Finite element methods applied to problems in fluid mechanics
65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs

Software:

deal.ii
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