Numerical analysis for two-phase flow with non-equilibrium capillary pressure in anisotropic porous media

In this paper, we are concerned with the convergence analysis of a combined finite volume-non-conforming finite element scheme, to approximate the two incompressible phase flow with dynamic capillary pressure in anisotropic porous media. All diffusion terms are anisotropic and heterogeneous and they are discretized by piecewise linear non-conforming triangular finite elements whereas the mobilities are discretized on dual diamond mesh. The mobilities are approximated by a non-standard way considering the inverse of the mean value of the inverse of mobilities across the interface of the dual mesh. This approximation ensures a priori estimates on the global pressure and on the water saturation. Under the assumption of non-degeneracry of mobilities, we prove the convergence of the combined scheme for the complete two-phase flow including the non-equilibrium capillary pressure.