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STABILIZED FINITE E...
STABILIZED FINITE ELEMENT APPROXIMATION OF THE MEAN CURVATURE VECTOR ON CLOSED SURFACES
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- Hansbo, Peter (author)
- Jönköping University,JTH, Produktutveckling,JTH. Forskningsmiljö Produktutveckling - Simulering och optimering
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- Larson, Mats G. (author)
- Umeå universitet,Institutionen för matematik och matematisk statistik,Umeå University
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- Zahedi, Sara (author)
- KTH,Numerisk analys, NA
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(creator_code:org_t)
- Society for Industrial and Applied Mathematics, 2015
- 2015
- English.
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In: SIAM Journal on Numerical Analysis. - : Society for Industrial and Applied Mathematics. - 0036-1429 .- 1095-7170. ; 53:4, s. 1806-1832
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Abstract
Subject headings
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- 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.
Subject headings
- NATURVETENSKAP -- Matematik (hsv//swe)
- NATURAL SCIENCES -- Mathematics (hsv//eng)
- NATURVETENSKAP -- Matematik -- Matematisk analys (hsv//swe)
- NATURAL SCIENCES -- Mathematics -- Mathematical Analysis (hsv//eng)
- NATURVETENSKAP -- Matematik -- Beräkningsmatematik (hsv//swe)
- NATURAL SCIENCES -- Mathematics -- Computational Mathematics (hsv//eng)
Keyword
- Laplace-Beltrami
- tangential calculus
- discrete curvature
- continuous interior penalty
Publication and Content Type
- ref (subject category)
- art (subject category)
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