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. © 2007 Elsevier Inc. All rights reserved.
On the parametric finite element approximation of evolving hypersurfaces in R3 / Barrett, J. W.; Garcke, H.; Nürnberg, R.. - In: JOURNAL OF COMPUTATIONAL PHYSICS. - ISSN 0021-9991. - 227:9(2008), pp. 4281-4307. [10.1016/j.jcp.2007.11.023]
On the parametric finite element approximation of evolving hypersurfaces in R3
Nürnberg R.
2008-01-01
Abstract
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. © 2007 Elsevier Inc. All rights reserved.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione
