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Cut finite element methods for elliptic problems on multipatch parametric surfaces
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics. (UMIT)
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics. (UMIT)
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics. (UMIT)ORCID iD: 0000-0001-7838-1307
2017 (English)In: Computer Methods in Applied Mechanics and Engineering, ISSN 0045-7825, E-ISSN 1879-2138, Vol. 324, 366-394 p.Article in journal (Refereed) Published
Abstract [en]

We develop a finite element method for the Laplace–Beltrami operator on a surface described by a set of patchwise parametrizations. The patches provide a partition of the surface and each patch is the image by a diffeomorphism of a subdomain of the unit square which is bounded by a number of smooth trim curves. A patchwise tensor product mesh is constructed by using a structured mesh in the reference domain. Since the patches are trimmed we obtain cut elements in the vicinity of the interfaces. We discretize the Laplace–Beltrami operator using a cut finite element method that utilizes Nitsche’s method to enforce continuity at the interfaces and a consistent stabilization term to handle the cut elements. Several quantities in the method are conveniently computed in the reference domain where the mappings impose a Riemannian metric. We derive a priori estimates in the energy and L2 norm and also present several numerical examples confirming our theoretical results.

Place, publisher, year, edition, pages
2017. Vol. 324, 366-394 p.
National Category
Computational Mathematics
Identifiers
URN: urn:nbn:se:umu:diva-138015DOI: 10.1016/j.cma.2017.06.018OAI: oai:DiVA.org:umu-138015DiVA: diva2:1129318
Available from: 2017-08-02 Created: 2017-08-02 Last updated: 2017-08-02

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Jonsson, TobiasLarson, Mats G.Larsson, Karl
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