JournalsifbVol. 4, No. 1pp. 89–109

A numerical scheme for axisymmetric solutions of curvature-driven free boundary problems, with applications to the Willmore flow

  • Uwe F. Mayer

    University of Utah, Salt Lake City, USA
  • Gieri Simonett

    Vanderbilt University, Nashville, USA
A numerical scheme for axisymmetric solutions of curvature-driven free boundary problems, with applications to the Willmore flow cover
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Abstract

We present a numerical scheme for axisymmetric solutions to curvature-driven moving boundary problems governed by a local law of motion, e.g. the mean curvature flow, the surface diffusion flow, and the Willmore flow. We then present several numerical experiments for the Willmore flow. In particular, we provide numerical evidence that the Willmore flow can develop singularities in finite time.

Cite this article

Uwe F. Mayer, Gieri Simonett, A numerical scheme for axisymmetric solutions of curvature-driven free boundary problems, with applications to the Willmore flow. Interfaces Free Bound. 4 (2002), no. 1, pp. 89–109

DOI 10.4171/IFB/54