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Dirichlet boundary value correction using Lagrange multipliers

Burman, E; Hansbo, P; Larson, MG; (2020) Dirichlet boundary value correction using Lagrange multipliers. BIT Numerical Mathematics , 60 pp. 235-260. 10.1007/s10543-019-00773-4. Green open access

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Abstract

We propose a boundary value correction approach for cases when curved boundaries are approximated by straight lines (planes) and Lagrange multipliers are used to enforce Dirichlet boundary conditions. The approach allows for optimal order convergence for polynomial order up to 3. We show the relation to a Taylor series expansion approach previously used in the context of Nitsche’s method and, in the case of inf-sup stable multiplier methods, prove a priori error estimates with explicit dependence on the meshsize and distance between the exact and approximate boundary.

Type: Article
Title: Dirichlet boundary value correction using Lagrange multipliers
Open access status: An open access version is available from UCL Discovery
DOI: 10.1007/s10543-019-00773-4
Publisher version: https://doi.org/10.1007/s10543-019-00773-4
Language: English
Additional information: Copyright © The Author(s) 2019. This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
Keywords: Boundary value correction, Lagrange multiplier, Dirichlet boundary conditions
UCL classification: UCL
UCL > Provost and Vice Provost Offices
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/10082483
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