# Asymptotic Behavior of systems of PDE arising in physics and biology: theoretical and numerical points of view (ABPDE II)

15-17 June 2016
Europe/Paris timezone

## Exponential decay of a finite volume scheme to the thermal equilibrium for drift-diffusion systems

17 Jun 2016, 14:40
45m
Salle de Réunion - Bâtiment M2 ()

### Speaker

Marianne Bessemoulin (Laboratoire de Mathématiques Jean Leray)

### Description

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.

### Presentation Materials

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