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CutFEM based on extended finite element spaces
Department of Mathematics, University College London, London, UK.
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.
2022 (English)In: Numerische Mathematik, ISSN 0029-599X, E-ISSN 0945-3245, Vol. 152, p. 331-369Article in journal (Refereed) Published
Abstract [en]

We develop a general framework for construction and analysis of discrete extension operators with application to unfitted finite element approximation of partial differential equations. In unfitted methods so called cut elements intersected by the boundary occur and these elements must in general by stabilized in some way. Discrete extension operators provides such a stabilization by modification of the finite element space close to the boundary. More, precisely the finite element space is extended from the stable interior elements over the boundary in a stable way which also guarantees optimal approximation properties. Our framework is applicable to all standard nodal based finite elements of various order and regularity. We develop an abstract theory for elliptic problems and associated parabolic time dependent partial differential equations and derive a priori error estimates. We finally apply this to some examples of partial differential equations of different order including the interface problems, the biharmonic operator and the sixth order triharmonic operator.

Place, publisher, year, edition, pages
Springer, 2022. Vol. 152, p. 331-369
Keywords [en]
65N30, 65N85
National Category
Mathematics
Identifiers
URN: urn:nbn:se:hj:diva-58559DOI: 10.1007/s00211-022-01313-zISI: 000855517700001Scopus ID: 2-s2.0-85138104101Local ID: HOA;intsam;834901OAI: oai:DiVA.org:hj-58559DiVA, id: diva2:1699911
Available from: 2022-09-29 Created: 2022-09-29 Last updated: 2022-12-09Bibliographically approved

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Hansbo, Peter

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