Numerical solutions for the surface diffusion flow in three space dimensions

Uwe F. Mayer

Abstract: The surface diffusion flow is a moving boundary problem that has a gradient flow structure. This gradient flow structure suggests an implicit finite differences approach to compute numerical solutions. The resulting numerical scheme will allow to compute the flow for any smooth orientable immersed initial surface. Observations include the loss of embeddedness for some initially embedded surface, the creation of singularities, and the long term behavior of solutions.

Key words:Numerical simulation, surface diffusion, mean curvature, gradient flow, free boundary problem, immersed hypersurface.

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