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Pré-Publication, Document De Travail Année : 2017

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

Résumé

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].
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Dates et versions

hal-01659418 , version 1 (08-12-2017)
hal-01659418 , version 2 (04-12-2018)

Identifiants

  • HAL Id : hal-01659418 , version 1

Citer

Marianne Bessemoulin-Chatard, Claire Chainais-Hillairet. Uniform-in-time Bounds for approximate Solutions of the drift-diffusion System. 2017. ⟨hal-01659418v1⟩

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