Section: New Results

Asymptotic Preserving numerical schemes for multiscale parabolic problems

In [45] , we consider a class of multiscale parabolic problems with diffusion coefficients oscillating in space at a possibly small scale $\epsilon$. Numerical homogenization methods are popular for such problems, because they capture efficiently the asymptotic behaviour as $\epsilon \to 0$, 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 $\epsilon \to 0$ and the non oscillatory regime $\epsilon \to 1$. 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.