Multiscale methods for problems with complex geometry

Daniel Elfverson, Mats G. Larson, Axel Målqvist

Published 2015-09-14Version 1

In this paper we extend the multiscale analysis to elliptic problems on complex domains, e.g. domains with cracks or complicated boundary. We construct corrected coarse test and trail spaces which takes the fine scale features of the domain into account. The corrections only needs to be computed in regions effected by the fine scale geometrical information of the domain. We achieve linear convergence rate in energy norm for the multiscale solution. Moreover, the conditioning of the multiscale method is not affected by how the domain boundary cuts the coarse elements in the background mesh. The analytical findings are verified in a series of numerical experiments.