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Multiscale methods for problems with complex geometry
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
2017 (English)In: Computer Methods in Applied Mechanics and Engineering, ISSN 0045-7825, E-ISSN 1879-2138, Vol. 321, 103-123 p.Article in journal (Refereed) Published
Abstract [en]

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.

Place, publisher, year, edition, pages
Elsevier, 2017. Vol. 321, 103-123 p.
Keyword [en]
multiscale method, complex geometry, a priori error bound
National Category
Computational Mathematics Mathematical Analysis
Identifiers
URN: urn:nbn:se:umu:diva-137377DOI: 10.1016/j.cma.2017.03.023ISI: 000402461100006OAI: oai:DiVA.org:umu-137377DiVA: diva2:1120660
Available from: 2017-07-06 Created: 2017-07-06 Last updated: 2017-07-06Bibliographically approved

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Elfverson, DanielLarson, Mats G.
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