RTkRTk mixed finite elements for some nonlinear problems

We show that the discrete operators and spaces of gradient discretizations can be designed so that the corresponding gradient scheme for a linear diffusion problem be identical to the Raviart–Thomas RTkRTk mixed finite element method for both the primal mixed finite element formulation and the hybrid dual formulation. We then give the hybrid dual RT0RT0 scheme for the approximation of a nonlinear model for two-phase flow in porous media; its convergence is then known thanks to a recent proof of the convergence of gradient schemes for this problem.