A numerical scheme for axisymmetric solutions of curvature driven free boundary problems, with applications to the Willmore flow
نویسندگان
چکیده
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.
منابع مشابه
A numerical scheme
Many moving boundary problems that are driven in some way by the curvature of the free boundary are gradient flows for the area of the moving interface. Examples are the Mullins-Sekerka flow, the Hele-Shaw flow, flow by mean curvature, and flow by averaged mean curvature. The gradient flow structure suggests an implicit finite differences approach to compute numerical solutions. The proposed nu...
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