Geodesic
A numerical scheme for axisymmetric solutions of curvature-driven free boundary problems, with applications to the Willmore flow
Uwe F. Mayer1 ; Gieri Simonett2
1University of Utah, Salt Lake City, USA
2Vanderbilt University, Nashville, USA
Interfaces and free boundaries, Tome 4 (2002) no. 1, pp. 89-109

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DOI

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.
DOI : 10.4171/ifb/54
Classification : 46-XX, 60-XX
Mots-clés : Willmore flow; numerical solutions; singularities

Uwe F. Mayer  1   ; Gieri Simonett  2

1 University of Utah, Salt Lake City, USA
2 Vanderbilt University, Nashville, USA 
Uwe F. Mayer; Gieri Simonett. A numerical scheme for axisymmetric solutions of curvature-driven free boundary problems, with applications to the Willmore flow. Interfaces and free boundaries, Tome 4 (2002) no. 1, pp. 89-109. doi: 10.4171/ifb/54
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     title = {A numerical scheme for axisymmetric solutions of curvature-driven free boundary problems, with applications to the {Willmore} flow},
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     year = {2002},
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     doi = {10.4171/ifb/54},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/ifb/54/}
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