Exponential decay of a finite volume scheme ...
Type de document :
Compte-rendu et recension critique d'ouvrage
DOI :
Titre :
Exponential decay of a finite volume scheme to the thermal equilibrium for drift–diffusion systems
Auteur(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]
Laboratoire de Mathématiques Jean Leray [LMJL]
Chainais-Hillairet, Claire [Auteur]
Reliable numerical approximations of dissipative systems [RAPSODI ]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Titre de la revue :
Journal of Numerical Mathematics
Pagination :
147-168
Éditeur :
De Gruyter
Date de publication :
2017-09
ISSN :
1570-2820
Discipline(s) HAL :
Mathématiques [math]/Analyse numérique [math.NA]
Résumé en anglais : [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 ...
Lire la suite >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.Lire moins >
Lire la suite >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.Lire moins >
Langue :
Anglais
Vulgarisation :
Non
Projet ANR :
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
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
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