Asymptotic behaviour of a finite-volume scheme for the transient drift-diffusion model
Claire Chainais-Hillairet, Francis Filbet · IMA Journal of Numerical Analysis · 2007
In this paper, we propose a finite-volume discretization for multidimensional nonlinear drift-diffusion system. Such a system arises in semiconductors modelling 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.