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A cut finite element method with boundary value correction
Department of Mathematics, University College London, London, United Kingdom.
Jönköping University, School of Engineering, JTH, Product Development. Jönköping University, School of Engineering, JTH. Research area Product Development - Simulation and Optimization.ORCID iD: 0000-0001-7352-1550
Department of Mathematics and Mathematical Statistics, Umeå University, Umeå, Sweden.
2018 (English)In: Mathematics of Computation, ISSN 0025-5718, E-ISSN 1088-6842, Vol. 87, no 310, p. 633-657Article in journal (Refereed) Published
Abstract [en]

In this contribution we develop a cut finite element method with boundary value correction of the type originally proposed by Bramble, Dupont, and Thomée in [Math. Comp. 26 (1972), 869-879]. The cut finite element method is a fictitious domain method with Nitsche-type enforcement of Dirichlet conditions together with stabilization of the elements at the boundary which is stable and enjoy optimal order approximation properties. A computational difficulty is, however, the geometric computations related to quadrature on the cut elements which must be accurate enough to achieve higher order approximation. With boundary value correction we may use only a piecewise linear approximation of the boundary, which is very convenient in a cut finite element method, and still obtain optimal order convergence. The boundary value correction is a modified Nitsche formulation involving a Taylor expansion in the normal direction compensating for the approximation of the boundary. Key to the analysis is a consistent stabilization term which enables us to prove stability of the method and a priori error estimates with explicit dependence on the meshsize and distance between the exact and approximate boundary.

Place, publisher, year, edition, pages
American Mathematical Society (AMS), 2018. Vol. 87, no 310, p. 633-657
National Category
Mathematics
Identifiers
URN: urn:nbn:se:hj:diva-38361DOI: 10.1090/mcom/3240ISI: 000418689600004Scopus ID: 2-s2.0-85038942183Local ID: JTHProduktutvecklingISOAI: oai:DiVA.org:hj-38361DiVA, id: diva2:1171523
Funder
Swedish Research Council, 2011-4992Swedish Research Council, 2013-4708Available from: 2018-01-08 Created: 2018-01-08 Last updated: 2018-01-08Bibliographically approved

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Hansbo, Peter

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