Numerical Validation of a Class of Mixed Discontinuous Galerkin Methods for Darcy Flow

In this paper we present a thorough set of numerical experiments to confirm the robustness of several Discontinuous Galerkin (DG) methods proposed for the approximation of Darcy law. We perform fairly twoand three-dimensional tests involving both low and high order approximations. Convergence tests carried out on Cartesian grids as well as on structured and unstructured triangular grids confirm the theoretical error estimates in the pressure energy norm and in the L norm of the velocity for both the symmetric and the non-symmetric DG schemes considered. Moreover, an optimal convergence rate in the L norm of the pressure error is observed in the cases where adjoint consistency does not hold, provided s = min{p+ 1, l} is odd, p and l being the polynomial degrees of the velocity and the pressure approximations, respectively. Test of accuracy and robustness involving a discontinuous permeability coefficient as well as a bounded smooth permeability function are also presented.