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Journal Articles Comptes Rendus. Mathématique Year : 2016

Asymptotic Preserving numerical schemes for multiscale parabolic problems

Abstract

We consider a class of multiscale parabolic problems with diffusion coefficients oscillating in space at a possibly small scale $\varepsilon$. Numerical homogenization methods are popular for such problems, because they capture efficiently the asymptotic behaviour as $\varepsilon \rightarrow 0$, without using a dramatically fine spatial discretization at the scale of the fast oscillations. However, known such homogenization schemes are in general not accurate for both the highly oscillatory regime $\varepsilon \rightarrow 0$ and the non oscillatory regime $\varepsilon \sim 1$. In this paper, we introduce an Asymptotic Preserving method based on an exact micro-macro decomposition of the solution which remains consistent for both regimes.

Dates and versions

hal-01187092 , version 1 (26-08-2015)

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Cite

Nicolas Crouseilles, Mohammed Lemou, Gilles Vilmart. Asymptotic Preserving numerical schemes for multiscale parabolic problems. Comptes Rendus. Mathématique, 2016, 354 (3), pp.271-276. ⟨10.1016/j.crma.2015.11.010⟩. ⟨hal-01187092⟩
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