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A cut discontinuous Galerkin method for the Laplace-Beltrami operator
University College London.
Jönköping University.
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.ORCID iD: 0000-0003-0803-9041
2017 (English)In: IMA Journal of Numerical Analysis, ISSN 0272-4979, E-ISSN 1464-3642, Vol. 37, no 1, 138-169 p.Article in journal (Refereed) Published
Abstract [en]

We develop a discontinuous cut finite element method for the Laplace–Beltrami operator on a hypersurface embedded in Rd . The method is constructed by using a discontinuous piecewise linear finite element space defined on a background mesh in Rd . The surface is approximated by a continuous piecewise linear surface that cuts through the background mesh in an arbitrary fashion. Then, a discontinuous Galerkin method is formulated on the discrete surface and in order to obtain coercivity, certain stabilization terms are added on the faces between neighbouring elements that provide control of the discontinuity as well as the jump in the gradient. We derive optimal a priori error and condition number estimates which are independent of the positioning of the surface in the background mesh. Finally, we present numerical examples confirming our theoretical results.

Place, publisher, year, edition, pages
2017. Vol. 37, no 1, 138-169 p.
Keyword [en]
surface PDE, Laplace–Beltrami, discontinuous Galerkin, cut finite element method
National Category
Computational Mathematics
Identifiers
URN: urn:nbn:se:umu:diva-130973DOI: 10.1093/imanum/drv068ISI: 000397147700005OAI: oai:DiVA.org:umu-130973DiVA: diva2:1070647
Available from: 2017-02-01 Created: 2017-02-01 Last updated: 2017-04-12Bibliographically approved

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Larson, Mats G.Massing, Andre
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Citation style
  • apa
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