Fully implicit discontinuous finite element methods for two-phase flow

In this paper we present two schemes based on discontinuous Galerkin methods for modeling fully implicit formulations of two-phase flow problems arising in porous media. Convergence with respect to uniform mesh refinement or increase in the polynomial degree are considered. Compared to sequential discontinuous schemes, our proposed schemes do not require slope limiting or upwind stabilization techniques. Numerical examples of homogeneous and heterogeneous media on structured and unstructured meshes show the robustness of the method.