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A stabilized cut finite element method for partial differential equations on surfaces : The Laplace-Beltrami operator
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- Burman, Erik (author)
- University College London
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- Hansbo, Peter (author)
- Jönköping University,JTH. Forskningsmiljö Produktutveckling - Simulering och optimering,JTH, Produktutveckling
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- Larson, Mats G. (author)
- Umeå universitet,Institutionen för matematik och matematisk statistik,Umeå University
- University College London JTH Forskningsmiljö Produktutveckling - Simulering och optimering (creator_code:org_t)
- Elsevier BV, 2015
- 2015
- English.
- In: Computer Methods in Applied Mechanics and Engineering. - : Elsevier BV. - 0045-7825 .- 1879-2138. ; 285, s. 188-207
- Journal article (peer-reviewed)
Abstract
Subject headings
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- 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.
Subject headings
- NATURVETENSKAP -- Matematik (hsv//swe)
- NATURAL SCIENCES -- Mathematics (hsv//eng)
- NATURVETENSKAP -- Matematik -- Beräkningsmatematik (hsv//swe)
- NATURAL SCIENCES -- Mathematics -- Computational Mathematics (hsv//eng)
Keyword
- Laplace-Beltrami
- Embedded surface
- Tangential calculus
Publication and Content Type
- ref (subject category)
- art (subject category)
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