Scientific article
Open access

Asymptotic Preserving numerical schemes for multiscale parabolic problems

Published inComptes rendus. Mathématique, vol. 354, no. 3, p. 271-276
Publication date2016

We consider a class of multiscale parabolic problems with diffusion coefficients oscillating in space at a possibly small scale ε . Numerical homogenization methods are popular for such problems, because they capture efficiently the asymptotic behavior as ε→0ε→0, without using a dramatically fine spatial discretization at the scale of the fast oscillations. However, it is known that such homogenization schemes are in general not accurate for both the highly oscillatory regime ε→0ε→0 and the non-oscillatory regime ε∼1ε∼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.

Citation (ISO format)
CROUSEILLES, Nicolas, LEMOU, Mohammed, VILMART, Gilles. Asymptotic Preserving numerical schemes for multiscale parabolic problems. In: Comptes rendus. Mathématique, 2016, vol. 354, n° 3, p. 271–276. doi: 10.1016/j.crma.2015.11.010
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Article (Accepted version)
ISSN of the journal1631-073X

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Creation02/23/2016 10:42:00 PM
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