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Graded Parametric CutFEM and CutIGA for Elliptic Boundary Value Problems in Domains with Corners
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.ORCID iD: 0000-0001-8981-0234
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.ORCID iD: 0000-0001-7838-1307
2019 (English)In: Computer Methods in Applied Mechanics and Engineering, ISSN 0045-7825, E-ISSN 1879-2138, Vol. 354, p. 331-350Article in journal (Refereed) Published
Abstract [en]

We develop a parametric cut finite element method for elliptic boundary value problems with corner singularities where we have weighted control of higher order derivatives of the solution to a neighborhood of a point at the boundary. Our approach is based on identification of a suitable mapping that grades the mesh towards the singularity. In particular, this mapping may be chosen without identifying the opening angle at the corner. We employ cut finite elements together with Nitsche boundary conditions and stabilization in the vicinity of the boundary. We prove that the method is stable and convergent of optimal order in the energy norm and L2 norm. This is achieved by mapping to the reference domain where we employ a structured mesh.

Place, publisher, year, edition, pages
Elsevier, 2019. Vol. 354, p. 331-350
Keywords [en]
Corner singularities, a priori error estimates, Cut finite element method, Cut isogeometric analysis
National Category
Computational Mathematics
Identifiers
URN: urn:nbn:se:umu:diva-159747DOI: 10.1016/j.cma.2019.05.024OAI: oai:DiVA.org:umu-159747DiVA, id: diva2:1320631
Funder
Swedish Foundation for Strategic Research , AM13-0029Swedish Research Council, 2013-4708Swedish Research Council, 2017-03911eSSENCE - An eScience Collaboration, -Available from: 2019-06-05 Created: 2019-06-05 Last updated: 2019-06-12Bibliographically approved
In thesis
1. Cut finite element methods on parametric multipatch surfaces
Open this publication in new window or tab >>Cut finite element methods on parametric multipatch surfaces
2019 (English)Licentiate thesis, comprehensive summary (Other academic)
Place, publisher, year, edition, pages
Umeå: Umeå Universitet, 2019. p. 23
Series
Research report in mathematics, ISSN 1653-0810
Keywords
Cut finite element method, Nitsche method, a priori error estimation
National Category
Computational Mathematics
Research subject
Mathematics
Identifiers
urn:nbn:se:umu:diva-159748 (URN)978-91-7855-019-7 (ISBN)
Presentation
2019-06-14, N420, Naturvetarhuset, Umeå, 13:00 (English)
Opponent
Supervisors
Available from: 2019-06-05 Created: 2019-06-05 Last updated: 2019-08-21Bibliographically approved

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Jonsson, TobiasLarson, Mats G.Larsson, Karl

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