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Finite element approximation of the Laplace–Beltrami operator on a surface with boundary

Burman, E; Hansbo, P; Larson, MG; Larsson, K; Massing, A; (2019) Finite element approximation of the Laplace–Beltrami operator on a surface with boundary. Numerische Mathematik , 141 (1) pp. 141-172. 10.1007/s00211-018-0990-2. Green open access

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Abstract

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 (Formula presented.) in the energy and (Formula presented.) norms that take the approximation of the surface and the boundary into account.

Type: Article
Title: Finite element approximation of the Laplace–Beltrami operator on a surface with boundary
Open access status: An open access version is available from UCL Discovery
DOI: 10.1007/s00211-018-0990-2
Publisher version: https://doi.org/10.1007/s00211-018-0990-2
Language: English
Additional information: This work is licensed under a Creative Commons Attribution 4.0 International License. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in the credit line; if the material is not included under the Creative Commons license, users will need to obtain permission from the license holder to reproduce the material. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/
UCL classification: UCL
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics
URI: https://discovery.ucl.ac.uk/id/eprint/10053685
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