Analysis of an interior penalty discontinuous Galerkin scheme for two phase flow in porous media with dynamic capillary effects

Abstract

We present an interior penalty discontinuous Galerkin scheme for a two-phase porous media flow model that incorporates dynamic effects in the capillary pressure. The approximation of the mass-conservation laws is performed in their original formulation, without introducing a global pressure. We prove the existence of a solution to the emerging fully discrete systems and the convergence of the scheme. Error-estimates are obtained for sufficiently smooth data.