Uniform-in-time Bounds for approximate Solutions of the drift-diffusion System

Bessemoulin-Chatard, Marianne; Chainais-Hillairet, Claire

Document type :

Article dans une revue scientifique: Article original

DOI :

10.1007/s00211-018-01019-1

Title :

Uniform-in-time Bounds for approximate Solutions of the drift-diffusion System

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 :

Numerische Mathematik

Pages :

881-916

Publisher :

Springer Verlag

Publication date :

2019

ISSN :

0029-599X

HAL domain(s) :

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

English abstract : [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 ...
Show more >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].Show less >

Language :

Anglais

Peer reviewed article :

Oui

Audience :

Internationale

Popular science :

Non

ANR Project :

Centre de Mathématiques Henri Lebesgue : fondements, interactions, applications et Formation

Collections :

Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL

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