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Discontinuous Galerkin Subgrid Finite Element Method for Heterogeneous Brinkman’s Equations

  • Oleg P. Iliev
  • Raytcho D. Lazarov
  • Joerg Willems
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5910)

Abstract

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.

Keywords

Numerical upscaling flow in heterogeneous porous media Brinkman’s equations subgrid approximation mixed FEM 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Oleg P. Iliev
    • 1
    • 2
  • Raytcho D. Lazarov
    • 2
    • 3
  • Joerg Willems
    • 1
    • 3
  1. 1.Fraunhofer ITWMKaiserslauternGermany
  2. 2.Inst. MathematicsBulgarian Academy of SciencesSofiaBulgaria
  3. 3.Dept. MathematicsTexas A&M UniversityCollege StationUSA

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