Study of a fully implicit scheme for the drift-diffusion system. Asymptotic behavior in the quasi-neutral limit

Abstract : In this paper, we are interested in the numerical approximation of the classical time-dependent drift-diffusion system near quasi-neutrality. We consider a fully implicit in time and finite volume in space scheme, where the convection-diffusion fluxes are approximated by Scharfetter-Gummel fluxes. We establish that all the a priori estimates needed to prove the convergence of the scheme does not depend on the Debye length $\lambda$. This proves that the scheme is asymptotic preserving in the quasi-neutral limit $\lambda \to 0$.
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Submitted on : Thursday, August 30, 2018 - 8:42:04 AM
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Marianne Bessemoulin-Chatard, Claire Chainais-Hillairet, Marie-Hélène Vignal. Study of a fully implicit scheme for the drift-diffusion system. Asymptotic behavior in the quasi-neutral limit. SIAM Journal on Numerical Analysis, Society for Industrial and Applied Mathematics, 2014, 52 (4), pp.1666-1691. ⟨10.1137/130913432⟩. ⟨hal-00801912v2⟩

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