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Low regularity estimates for CutFEM approximations of an elliptic problem with mixed boundary conditions
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.
2024 (English)In: Mathematics of Computation, ISSN 0025-5718, E-ISSN 1088-6842, Vol. 93, no 345, p. 35-54Article in journal (Refereed) Published
Abstract [en]

We show error estimates for a cut finite element approximation of a second order elliptic problem with mixed boundary conditions. The error estimates are of low regularity type where we consider the case when the exact solution u & ISIN; Hs with s & ISIN; (1, 3/2]. For Nitsche type methods this case requires special handling of the terms involving the normal flux of the exact solution at the the boundary. For Dirichlet boundary conditions the estimates are optimal, whereas in the case of mixed Dirichlet-Neumann boundary conditions they are suboptimal by a logarithmic factor.

Place, publisher, year, edition, pages
American Mathematical Society (AMS), 2024. Vol. 93, no 345, p. 35-54
National Category
Mathematics
Identifiers
URN: urn:nbn:se:hj:diva-62377DOI: 10.1090/mcom/3875ISI: 001047664700001Scopus ID: 2-s2.0-85174930720Local ID: ;intsam;901188OAI: oai:DiVA.org:hj-62377DiVA, id: diva2:1793934
Funder
Swedish Research Council, 2017-03911, 2018-05262, 2021-04925Available from: 2023-09-04 Created: 2023-09-04 Last updated: 2023-11-06Bibliographically approved

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Hansbo, Peter

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