Positive control volume finite element scheme for a degenerate compressible two-phase flow in anisotropic porous media

My talk is about the convergence analysis of a positive control volume finite element scheme (CVFE) for a degenerate compressible two-phase flow model in porous media. An implicit Euler scheme in time and a CVFE discretisation in space are used to discretize the equations of the model. The maximum principle and energy estimates are fulfilled without any constraint on stiffness coefficients. We then establish that any sequence of solutions converges to a weak solution of the continuous problem, up to a subsequence, as the size of the mesh tends to zero. Numerical tests are presented in two dimensional space to show the behavior of the water saturation and the gas pressure.