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

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.