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arXiv · 1507.06394

Asymptotic Preserving numerical schemes for multiscale parabolic problems

Nicolas Crouseilles·Mohammed Lemou·Gilles Vilmart
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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.

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Nicolas Crouseilles, Mohammed Lemou, Gilles Vilmart. 2015-07-23. Asymptotic Preserving numerical schemes for multiscale parabolic problems. https://doi.org/10.1016/j.crma.2015.11.010

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