Section: New Results
Asymptotic Preserving numerical schemes for multiscale parabolic problems
In  , we consider a class of multiscale parabolic problems with diffusion coefficients oscillating in space at a possibly small scale . Numerical homogenization methods are popular for such problems, because they capture efficiently the asymptotic behaviour as , 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 and the non oscillatory regime . 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.