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Discontinuous galerkin subgrid finite element method for heterogeneous Brinkman's equations

: Iliev, O.P.; Lazarov, R.D.; Willems, J.


Lirkov, I. (Hrsg.):
Large-scale scientific computing. 7th international conference (LSSC 2009) : Sozopol, Bulgaria, June 4-8, 2009
Berlin: Springer, 2010 (Lecture Notes in Computer Science 5910)
ISBN: 3-642-12534-4 (print)
ISBN: 978-3-642-12534-8 (print)
ISBN: 978-3-642-12535-5 (online)
DOI: 10.1007/978-3-642-12535-5
ISSN: 0302-9743
International Conference on Large-Scale Scientific Computions (LSSC) <7, 2009, Sozopol>
Conference Paper
Fraunhofer ITWM ()

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 Wang and Ye in [12] and the concept of subgrid approximation developed for Darcy’s equations by Arbogast in [4]. 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, [7], and we present the computational results for a number of model problems.