Marianne Bessemoulin (Laboratoire de Mathématiques Jean Leray)
We are interested in the large-time behavior of a numerical scheme discretizing drift-diffusion systems for semiconductors. The considered scheme is finite volume in space, and the numerical fluxes are a generalization of the classical Scharfetter-Gummel scheme, which allows to consider both linear or nonlinear pressure laws. We study the convergence of approximate solutions towards an approximation of the thermal equilibrium state as time tends to infinity, and obtain a decay rate by controlling the discrete relative entropy with the entropy production. This result is proved under assumptions of existence and uniform-in-time $L^\infty$ estimates for numerical solutions, which will be discussed. This is a joined work with Claire Chainais-Hillairet.