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Fictitious domain method with boundary value correction using penalty-free Nitsche method
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
2018 (English)In: Journal of Numerical Mathematics, ISSN 1570-2820, E-ISSN 1569-3953, Vol. 26, no 2, p. 77-95Article in journal (Refereed) Published
Abstract [en]

In this paper, we consider a fictitious domain approach based on a Nitsche type method without penalty. To allow for high order approximation using piecewise affine approximation of the geometry we use a boundary value correction technique based on Taylor expansion from the approximate to the physical boundary. To ensure stability of the method a ghost penalty stabilization is considered in the boundary zone. We prove optimal error estimates in the H1-norm and estimates suboptimal by 𝓞(h1/2) in the L2-norm. The suboptimality is due to the lack of adjoint consistency of our formulation. Numerical results are provided to corroborate the theoretical study.

Place, publisher, year, edition, pages
Walter de Gruyter, 2018. Vol. 26, no 2, p. 77-95
Keywords [en]
Nitsche's method, fictitious domain method, boundary value correction
National Category
Computational Mathematics
Identifiers
URN: urn:nbn:se:umu:diva-150874ISI: 000435979300002Scopus ID: 2-s2.0-8504415940OAI: oai:DiVA.org:umu-150874DiVA, id: diva2:1244373
Available from: 2018-08-31 Created: 2018-08-31 Last updated: 2018-08-31Bibliographically approved

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Larson, Mats G.

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