Barrett, John W. and Garcke, Harald and Nürnberg, Robert (2007) On the parametric finite element approximation of evolving hypersurfaces in R³. SIAM Journal on Scientific Computing 29 (3), pp. 1006-1041.
Other URL: http://link.aip.org/link/?SCE/29/1006/1
We present a variational formulation of motion by minus the Laplacian of curvature and mean curvature flow, as well as related second and fourth order flows of a
closed hypersurface in R³. On introducing a parametric finite element approximation, we prove stability bounds and compare our scheme with existing approaches. The presented scheme has very good properties with respect to the distribution of mesh points and, if applicable, volume conservation.
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|Date:||10 May 2007|
|Institutions:||Mathematics > Prof. Dr. Harald Garcke|
|Dewey Decimal Classification:||500 Science > 510 Mathematics|
|Refereed:||Yes, this version has been refereed|
|Created at the University of Regensburg:||Yes|
|Deposited On:||19 Jan 2007|
|Last Modified:||13 Mar 2014 09:42|