An adaptive multiscale finite element method
Loading...
Date
2012-08-08
Journal Title
Journal ISSN
Volume Title
Publisher
Abstract
This work is devoted to an adaptive multiscale finite element method
(MsFEM) for solving elliptic problems with rapidly oscillating coeefficients.
Starting from a general version of the MsFEM with oversampling, we de-
rive an a posteriori estimate for the H1-error between the exact solution
of the problem and a corresponding MsFEM approximation. Our esti-
mate holds without any assumptions on scale separation or on the type of
the heterogeneity. The estimator splits into different contributions which
account for the coarse grid error, the fine grid error and the oversampling
error. Based on the error estimate we construct an adaptive algorithm
that is validated in numerical experiments.