Multiscale methods for problems with complex geometry
Journal article, 2017

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.

priori error bound

multiscale method

complex geometry


Daniel Elfverson

Umeå University

Mats G Larson

Umeå University

Axel Målqvist

Chalmers, Mathematical Sciences, Applied Mathematics and Statistics

Chalmers, Mathematical Sciences

University of Gothenburg

Computer Methods in Applied Mechanics and Engineering

0045-7825 (ISSN)

Vol. 321 103-123

Subject Categories



Areas of Advance

Building Futures (2010-2018)


Basic sciences



More information

Latest update