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Dirichlet boundary value correction using Lagrange multipliers
Department of Mathematics, University College London, London, United Kingdom.
Jönköping University, School of Engineering, JTH, Materials and Manufacturing.ORCID iD: 0000-0001-7352-1550
Department of Mathematics and Mathematical Statistics, Umeå University, Umeå, Sweden.
2019 (English)In: BIT Numerical Mathematics, ISSN 0006-3835, E-ISSN 1572-9125Article in journal (Refereed) Epub ahead of print
Abstract [en]

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. 

Place, publisher, year, edition, pages
Springer, 2019.
Keywords [en]
Boundary value correction, Dirichlet boundary conditions, Lagrange multiplier
National Category
Mathematics
Identifiers
URN: urn:nbn:se:hj:diva-46297DOI: 10.1007/s10543-019-00773-4Scopus ID: 2-s2.0-85072217688Local ID: ;JTHMaterialISOAI: oai:DiVA.org:hj-46297DiVA, id: diva2:1353320
Available from: 2019-09-23 Created: 2019-09-23 Last updated: 2019-09-23

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Hansbo, Peter

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