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Cut finite element methods for elliptic problems on multipatch parametric surfaces
Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik. (UMIT)
Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik. (UMIT)
Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik. (UMIT)ORCID-id: 0000-0001-7838-1307
2017 (engelsk)Inngår i: Computer Methods in Applied Mechanics and Engineering, ISSN 0045-7825, E-ISSN 1879-2138, Vol. 324, s. 366-394Artikkel i tidsskrift (Fagfellevurdert) 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.

sted, utgiver, år, opplag, sider
Elsevier, 2017. Vol. 324, s. 366-394
Emneord [en]
Cut finite elements, Fictitious domain, Nitsche's method, A priori error estimates, Multipatch surface, Laplace-Beltrami operator
HSV kategori
Identifikatorer
URN: urn:nbn:se:umu:diva-138015DOI: 10.1016/j.cma.2017.06.018ISI: 000408032700016OAI: oai:DiVA.org:umu-138015DiVA, id: diva2:1129318
Tilgjengelig fra: 2017-08-02 Laget: 2017-08-02 Sist oppdatert: 2019-06-05bibliografisk kontrollert
Inngår i avhandling
1. Cut finite element methods on parametric multipatch surfaces
Åpne denne publikasjonen i ny fane eller vindu >>Cut finite element methods on parametric multipatch surfaces
2019 (engelsk)Licentiatavhandling, med artikler (Annet vitenskapelig)
sted, utgiver, år, opplag, sider
Umeå: Umeå Universitet, 2019. s. 23
Serie
Research report in mathematics, ISSN 1653-0810
Emneord
Cut finite element method, Nitsche method, a priori error estimation
HSV kategori
Forskningsprogram
matematik
Identifikatorer
urn:nbn:se:umu:diva-159748 (URN)978-91-7855-019-7 (ISBN)
Presentation
2019-06-14, N420, Naturvetarhuset, Umeå, 13:00 (engelsk)
Opponent
Veileder
Tilgjengelig fra: 2019-06-05 Laget: 2019-06-05 Sist oppdatert: 2019-08-21bibliografisk kontrollert

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