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Stabilized finite element approximation of the mean curvature vector on closed surfaces
Jönköping University, School of Engineering, JTH, Product Development. Jönköping University, School of Engineering, JTH. Research area Product Development - Simulation and Optimization.
Umeå University.
KTH.
2015 (English)In: SIAM Journal on Numerical Analysis, ISSN 0036-1429, E-ISSN 1095-7170, Vol. 53, no 4, p. 1806-1832Article in journal (Refereed) Published
Abstract [en]

The mean curvature vector of a surface is obtained by letting the Laplace--Beltrami operator act on the embedding of the surface in R^3. In this contribution we develop a stabilized finite element approximation of the mean curvature vector of certain piecewise linear surfaces which enjoys first order convergence in L^2. The stabilization involves the jump in the tangent gradient in the direction of the outer co-normals at each edge in the surface mesh. We consider both standard meshed surfaces and so-called cut surfaces that are level sets of piecewise linear distance functions. We prove a priori error estimates and verify the theoretical results numerically.

Place, publisher, year, edition, pages
2015. Vol. 53, no 4, p. 1806-1832
National Category
Computational Mathematics
Identifiers
URN: urn:nbn:se:hj:diva-27624DOI: 10.1137/140982696ISI: 000360692100008Scopus ID: 2-s2.0-84941032182OAI: oai:DiVA.org:hj-27624DiVA, id: diva2:843027
Funder
Swedish Foundation for Strategic Research , AM13-0029Swedish Research Council, 2011-4992Swedish Research Council, 2013-4708Available from: 2015-07-24 Created: 2015-07-24 Last updated: 2017-12-04Bibliographically approved

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Hansbo, Peter

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