Numerical validation of a class of mixed discontinuous Galerkin methods for Darcy flow

We present a thorough set of numerical experiments to confirm the robustness of several discontinuous Galerkin methods proposed for the approximation of Darcy law. We perform two- and three-dimensional tests involving both low and high order approximations on Cartesian grids and on triangular grids. The tests we present confirm the theoretical estimates for symmetric approximations and characterize the behavior of non-symmetric approximations, where convergence rates that are one order better than predicted are observed for suitable choices of approximation spaces. Robustness and accuracy of all these methods are assessed for realistic numerical experiments where discontinuous permeability coefficients and bounded smooth permeability functions are used.