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Finite element approximation of the Laplace-Beltrami operator on a surface with boundary
University College London, UK, Department of Mathematics.
Jönköping University, School of Engineering, JTH, Product Development.ORCID iD: 0000-0001-7352-1550
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.ORCID iD: 0000-0001-5589-4521
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics. (UMIT)ORCID iD: 0000-0001-7838-1307
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2019 (English)In: Numerische Mathematik, ISSN 0029-599X, E-ISSN 0945-3245, Vol. 141, no 1, p. 141-172Article in journal (Refereed) Published
Abstract [en]

We develop a finite element method for the Laplace–Beltrami operator on a surface with boundary and nonhomogeneous Dirichlet boundary conditions. The method is based on a triangulation of the surface and the boundary conditions are enforced weakly using Nitsche's method. We prove optimal order a priori error estimates for piecewise continuous polynomials of order k ≥ 1 in the energy and L2 norms that take the approximation of the surface and the boundary into account.

Place, publisher, year, edition, pages
Springer, 2019. Vol. 141, no 1, p. 141-172
National Category
Computational Mathematics
Identifiers
URN: urn:nbn:se:umu:diva-155591DOI: 10.1007/s00211-018-0990-2ISI: 000457025700005OAI: oai:DiVA.org:umu-155591DiVA, id: diva2:1282092
Funder
Swedish Research Council, 2011-4992, 2013-4708eSSENCE - An eScience CollaborationAvailable from: 2019-01-24 Created: 2019-01-24 Last updated: 2019-02-20Bibliographically approved

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Hansbo, PeterLarson, Mats G.Larsson, KarlMassing, Andre
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