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A stabilized cut finite element method for partial differential equations on surfaces: The Laplace-Beltrami operator
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
2015 (English)In: Computer Methods in Applied Mechanics and Engineering, ISSN 0045-7825, E-ISSN 1879-2138, Vol. 285, 188-207 p.Article in journal (Refereed) Published
Abstract [en]

We consider solving the Laplace-Beltrami problem on a smooth two dimensional surface embedded into a three dimensional space meshed with tetrahedra. The mesh does not respect the surface and thus the surface cuts through the elements. We consider a Galerkin method based on using the restrictions of continuous piecewise linears defined on the tetrahedra to the surface as trial and test functions. The resulting discrete method may be severely ill-conditioned, and the main purpose of this paper is to suggest a remedy for this problem based on adding a consistent stabilization term to the original bilinear form. We show optimal estimates for the condition number of the stabilized method independent of the location of the surface. We also prove optimal a priori error estimates for the stabilized method. (c) 2014 Elsevier B.V. All rights reserved.

Place, publisher, year, edition, pages
2015. Vol. 285, 188-207 p.
Keyword [en]
Laplace-Beltrami, Embedded surface, Tangential calculus
National Category
URN: urn:nbn:se:umu:diva-100942DOI: 10.1016/j.cma.2014.10.044ISI: 000349637700009OAI: diva2:796700
Available from: 2015-03-20 Created: 2015-03-16 Last updated: 2015-03-20Bibliographically approved

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Larson, Mats G.
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Department of Mathematics and Mathematical Statistics
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