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Asymptotic Preserving numerical schemes for multiscale parabolic problems

Crouseilles, Nicolas
Lemou, Mohammed
Published in Comptes rendus. Mathématique. 2016, vol. 354, no. 3, p. 271-276
Abstract 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.
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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 https://archive-ouverte.unige.ch/unige:80936

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Deposited on : 2016-02-24

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