Title :

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

Author(s) :

Bessemoulin-Chatard, Marianne [Auteur]
Laboratoire de Mathématiques Jean Leray [LMJL]
Chainais-Hillairet, Claire [Auteur]
Reliable numerical approximations of dissipative systems [RAPSODI]
Laboratoire Paul Painlevé - UMR 8524 [LPP]

Journal title :

Journal of Numerical Mathematics

Pages :

147-168

Publisher :

De Gruyter

Publication date :

2017-09

ISSN :

1570-2820

HAL domain(s) :

Mathématiques [math]/Analyse numérique [math.NA]

English abstract : [en]

In this paper, we study the large–time behavior of a numerical scheme discretizing drift– diffusion systems for semiconductors. The numerical method is finite volume in space, implicit in time, and the numerical fluxes are ...
Show more >In this paper, we study the large–time behavior of a numerical scheme discretizing drift– diffusion systems for semiconductors. The numerical method is finite volume in space, implicit in time, 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 $L ∞$ estimates for numerical solutions, which are then discussed. We conclude by presenting some numerical illustrations of the stated results.Show less >

Language :

Anglais

Popular science :

Non

ANR Project :

Nouveaux schémas numériques pour des phénomènes géophysiques extrêmes
Capture de l'Asymptotique pour des Systèmes Hyperboliques de Lois de Conservation avec Termes Source
MOdèles, Oscillations et SchEmas NUmeriques
Centre de Mathématiques Henri Lebesgue : fondements, interactions, applications et Formation

Collections :

• Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL