Finite volume approximation for degenerate drift-diffusion system in several space dimensions

This paper is devoted to a finite volume discretization for multidimensional nonlinear drift-diffusion system. Such system arises in semiconductors modelling and is composed of two degenerate parabolic equations and an elliptic one. We prove the convergence of the finite volume scheme and then the existence of solutions to the problem. Several numerical tests show the efficiency of the method.