Uniform-in-time Bounds for approximate ...
Type de document :
Article dans une revue scientifique: Article original
Titre :
Uniform-in-time Bounds for approximate Solutions of the drift-diffusion System
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 :
Numerische Mathematik
Pagination :
881-916
Éditeur :
Springer Verlag
Date de publication :
2019
ISSN :
0029-599X
Discipline(s) HAL :
Mathématiques [math]/Analyse numérique [math.NA]
Résumé en anglais : [en]
In this paper, we consider a numerical approximation of the Van Roosbroeck's drift– diffusion system given by a backward Euler in time and finite volume in space discretization, with Scharfetter-Gummel fluxes. We first ...
Lire la suite >In this paper, we consider a numerical approximation of the Van Roosbroeck's drift– diffusion system given by a backward Euler in time and finite volume in space discretization, with Scharfetter-Gummel fluxes. We first propose a proof of existence of a solution to the scheme which does not require any assumption on the time step. The result relies on the application of a topological degree argument which is based on the positivity and on uniform-in-time upper bounds of the approximate densities. Secondly, we establish uniform-in-time lower bounds satisfied by the approximate densities. These uniform-in-time upper and lower bounds ensure the exponential decay of the scheme towards the thermal equilibrium as shown in [3].Lire moins >
Lire la suite >In this paper, we consider a numerical approximation of the Van Roosbroeck's drift– diffusion system given by a backward Euler in time and finite volume in space discretization, with Scharfetter-Gummel fluxes. We first propose a proof of existence of a solution to the scheme which does not require any assumption on the time step. The result relies on the application of a topological degree argument which is based on the positivity and on uniform-in-time upper bounds of the approximate densities. Secondly, we establish uniform-in-time lower bounds satisfied by the approximate densities. These uniform-in-time upper and lower bounds ensure the exponential decay of the scheme towards the thermal equilibrium as shown in [3].Lire moins >
Langue :
Anglais
Comité de lecture :
Oui
Audience :
Internationale
Vulgarisation :
Non
Projet ANR :
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