Error analysis for a finite difference scheme for axisymmetric mean curvature flow of genus-0 surfaces

10/19/2020

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by   Klaus Deckelnick, et al.

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We consider a finite difference approximation of mean curvature flow for axisymmetric surfaces of genus zero. A careful treatment of the degeneracy at the axis of rotation for the one dimensional partial differential equation for a parameterization of the generating curve allows us to prove error bounds with respect to discrete L^2– and H^1–norms for a fully discrete approximation. The theoretical results are confirmed with the help of numerical convergence experiments. We also present numerical simulations for some genus-0 surfaces, including for a non-embedded self-shrinker for mean curvature flow.