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Multiscale methods for problems with complex geometry

Journal article
Authors Daniel Elfverson
Mats G. Larson
Axel Målqvist
Published in Computer Methods in Applied Mechanics and Engineering
Volume 321
Pages 103-123
ISSN 0045-7825
Publication year 2017
Published at Department of Mathematical Sciences
Pages 103-123
Language en
Links https://doi.org/10.1016/j.cma.2017....
Keywords a priori error bound, complex geometry, multiscale method
Subject categories Computational Mathematics, Applied mathematics

Abstract

© 2017 Elsevier B.V. We propose a multiscale method for elliptic problems on complex domains, e.g. domains with cracks or complicated boundary. For local singularities this paper also offers a discrete alternative to enrichment techniques such as XFEM. We construct corrected coarse test and trail spaces which takes the fine scale features of the computational domain into account. The corrections only need to be computed in regions surrounding fine scale geometric features. We achieve linear convergence rate in the energy norm for the multiscale solution. Moreover, the conditioning of the resulting matrices is not affected by the way the domain boundary cuts the coarse elements in the background mesh. The analytical findings are verified in a series of numerical experiments.

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