  We apply geometric multigrid methods for the finite element approximation of
flow problems governed by Darcy and Brinkman systems used in modeling highly
heterogeneous porous media. The method is based on divergence-conforming
discontinuous Galerkin methods and overlapping, patch based domain
decomposition smoothers. We show in benchmark experiments that the method is
robust with respect to mesh size and contrast of permeability for highly
heterogeneous media.
