Study of a fully implicit scheme for the drift-diffusion system. Asymptotic behavior in the quasi-neutral limit.

Marianne Bessemoulin-Chatard (1) , Claire Chainais-Hillairet (2, 3) , Marie-Hélène Vignal (4)

1 MMCS - Modélisation mathématique, calcul scientifique
2 MEPHYSTO - Quantitative methods for stochastic models in physics
3 LPP - Laboratoire Paul Painlevé - UMR 8524
4 IMT - Institut de Mathématiques de Toulouse UMR5219

In this paper, we are interested in the numerical approximation of the classical time-dependent drift-diffusion system near quasi-neutrality. We consider a fully implicit in time and finite volume in space scheme, where the convection-diffusion fluxes are approximated by Scharfetter-Gummel fluxes. We establish that all the a priori estimates needed to prove the convergence of the scheme does not depend on the Debye length. This proves that the scheme is asymptotic preserving in the quasi-neutral limit.

Mots clés: quasi-neutral limit; drift-diffusion; entropy method; asymptotic preserving schemes; finite volume

Domaines: Analyse numérique [math.NA]

Marianne Bessemoulin-Chatard, Claire Chainais-Hillairet, Marie-Hélène Vignal. Study of a fully implicit scheme for the drift-diffusion system. Asymptotic behavior in the quasi-neutral limit.. SIAM Journal on Numerical Analysis, 2014, 52 (4), pp.1666-1691. ⟨hal-00801912v1⟩