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A Nitsche method for elliptic problems on composite surfaces
Jönköping University.
Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
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. 326, s. 505-525Artikkel i tidsskrift (Fagfellevurdert) Published
Abstract [en]

We develop a finite element method for elliptic partial differential equations on so called composite surfaces that are built up out of a finite number of surfaces with boundaries that fit together nicely in the sense that the intersection between any two surfaces in the composite surface is either empty, a point, or a curve segment, called an interface curve. Note that several surfaces can intersect along the same interface curve. On the composite surface we consider a broken finite element space which consists of a continuous finite element space at each subsurface without continuity requirements across the interface curves. We derive a Nitsche type formulation in this general setting and by assuming only that a certain inverse inequality and an approximation property hold we can derive stability and error estimates in the case when the geometry is exactly represented. We discuss several different realizations, including so called cut meshes, of the method. Finally, we present numerical examples.

sted, utgiver, år, opplag, sider
Lausanne: Elsevier, 2017. Vol. 326, s. 505-525
Emneord [en]
Nitsche method, Composite surfaces, Laplace-Beltrami operator, A priori error estimates
HSV kategori
Identifikatorer
URN: urn:nbn:se:umu:diva-139526DOI: 10.1016/j.cma.2017.08.033ISI: 000413322300022OAI: oai:DiVA.org:umu-139526DiVA, id: diva2:1141674
Forskningsfinansiär
Swedish Research Council, 2011-4992Swedish Research Council, 2013-4708eSSENCE - An eScience CollaborationSwedish Foundation for Strategic Research , AM13-0029Tilgjengelig fra: 2017-09-15 Laget: 2017-09-15 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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