On the parametric finite element approximation of evolving hypersurfaces in R3

Authors:
John W. Barrett;Harald Garcke;Robert Nürnberg
Affiliations:
Department of Mathematics, Imperial College London, London SW7 2AZ, UK;NWF I - Mathematik, Universität Regensburg, 93040 Regensburg, Germany;Department of Mathematics, Imperial College London, London SW7 2AZ, UK
Venue:
Journal of Computational Physics
Year:
2008

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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 R^3. 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.