STABILIZED FINITE ELEMENT APPROXIMATION OF THE MEAN CURVATURE VECTOR ON CLOSED SURFACES
2015 (English)In: SIAM Journal on Numerical Analysis, ISSN 0036-1429, E-ISSN 1095-7170, Vol. 53, no 4, 1806-1832 p.Article in journal (Refereed) Published
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, 1806-1832 p.
Laplace-Beltrami, tangential calculus, discrete curvature, continuous interior penalty
IdentifiersURN: urn:nbn:se:umu:diva-109823DOI: 10.1137/140982696ISI: 000360692100008OAI: oai:DiVA.org:umu-109823DiVA: diva2:859215