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A note on the stability parameter in Nitsche's method for unfitted boundary value problems
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
2018 (English)In: Computers and Mathematics with Applications, ISSN 0898-1221, E-ISSN 1873-7668, Vol. 75, no 12, p. 4322-4336Article in journal (Refereed) Published
Abstract [en]

Nitsche's method is a popular approach to implement Dirichlet-type boundary conditions in situations where a strong imposition is either inconvenient or simply not feasible. The method is widely applied in the context of unfitted finite element methods. Of the classical (symmetric) Nitsche's method it is well-known that the stabilization parameter in the method has to be chosen sufficiently large to obtain unique solvability of discrete systems. In this short note we discuss an often used strategy to set the stabilization parameter and describe a possible problem that can arise from this. We show that in specific situations error bounds can deteriorate and give examples of computations where Nitsche's method yields large and even diverging discretization errors. 

Place, publisher, year, edition, pages
Elsevier, 2018. Vol. 75, no 12, p. 4322-4336
Keywords [en]
Nitsche's method, Unfitted/immersed finite element methods, Stabilization/penalty parameter, curacy, Stability, Error analysis
National Category
Computational Mathematics
Identifiers
URN: urn:nbn:se:umu:diva-148714DOI: 10.1016/j.camwa.2018.03.032ISI: 000432886400011Scopus ID: 2-s2.0-85045224009OAI: oai:DiVA.org:umu-148714DiVA, id: diva2:1221118
Funder
Swedish Research Council, 2017-05038Available from: 2018-06-19 Created: 2018-06-19 Last updated: 2018-06-19Bibliographically approved

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Massing, André

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