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A cut finite element method for the Bernoulli free boundary value problem
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
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2017 (English)In: Computer Methods in Applied Mechanics and Engineering, ISSN 0045-7825, E-ISSN 1879-2138, Vol. 317, 598-618 p.Article in journal (Refereed) Published
Abstract [en]

We develop a cut finite element method for the Bernoulli free boundary problem. The free boundary, represented by an approximate signed distance function on a fixed background mesh, is allowed to intersect elements in an arbitrary fashion. This leads to so called cut elements in the vicinity of the boundary. To obtain a stable method, stabilization terms are added in the vicinity of the cut elements penalizing the gradient jumps across element sides. The stabilization also ensures good conditioning of the resulting discrete system. We develop a method for shape optimization based on moving the distance function along a velocity field which is computed as the H-1 Riesz representation of the shape derivative. We show that the velocity field is the solution to an interface problem and we prove an a priori error estimate of optimal order, given the limited regularity of the velocity field across the interface, for the velocity field in the H-1 norm. Finally, we present illustrating numerical results.

Place, publisher, year, edition, pages
2017. Vol. 317, 598-618 p.
Keyword [en]
Free boundary value problem, CutFEM, Shape optimization, Level set, Fictitious domain method
National Category
Computational Mathematics
Identifiers
URN: urn:nbn:se:umu:diva-133720DOI: 10.1016/j.cma.2016.12.021ISI: 000398373500024OAI: oai:DiVA.org:umu-133720DiVA: diva2:1093240
Available from: 2017-05-05 Created: 2017-05-05 Last updated: 2017-05-05Bibliographically approved

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Elfverson, DanielLarson, Mats G.Larsson, Karl
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CiteExportLink to record
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Citation style
  • apa
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  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
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  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
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  • asciidoc
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