Asymptotic behavior of a finite volume scheme for the transient drift-diffusion model
Résumé
In this paper, we propose a finite volume discretization for multidimensional nonlinear drift-diffusion system. Such a system arises in semi-conductors modeling and is composed of two parabolic equations and an elliptic one. We prove that the numerical solution converges to a steady state when time goes to infinity. Several numerical tests show the efficiency of the method.