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Minimal surface computation using a finite element method on an embedded surface
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
2015 (English)In: International Journal for Numerical Methods in Engineering, ISSN 0029-5981, E-ISSN 1097-0207, Vol. 104, no 7, 502-512 p.Article in journal (Refereed) Published
Abstract [en]

We suggest a finite element method for finding minimal surfaces based on computing a discrete Laplace-Beltrami operator operating on the coordinates of the surface. The surface is a discrete representation of the zero level set of a distance function using linear tetrahedral finite elements, and the finite element discretization is carried out on the piecewise planar isosurface using the shape functions from the background three-dimensional mesh used to represent the distance function. A recently suggested stabilized scheme for finite element approximation of the mean curvature vector is a crucial component of the method.

Place, publisher, year, edition, pages
2015. Vol. 104, no 7, 502-512 p.
Keyword [en]
mean curvature, Laplace-Beltrami operator, level set, ghost penalty stabilization
National Category
Geometry
Identifiers
URN: urn:nbn:se:umu:diva-110975DOI: 10.1002/nme.4892ISI: 000362552500003OAI: oai:DiVA.org:umu-110975DiVA: diva2:872447
Available from: 2015-11-19 Created: 2015-11-02 Last updated: 2015-11-19Bibliographically approved

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Larson, Mats G.
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Department of Mathematics and Mathematical Statistics
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