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 onedimensional partial differential equation for a parameterization of the generating curve allows us to prove error bounds with respect to discrete L2 - and H1 -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 nonembedded self-shrinker for mean curvature flow
Error Analysis for a Finite Difference Scheme for Axisymmetric Mean Curvature Flow of Genus-0 Surfaces / Deckelnick, Klaus; Nürnberg, Robert. - In: SIAM JOURNAL ON NUMERICAL ANALYSIS. - ISSN 0036-1429. - 59:5(2021), pp. 2698-2721. [10.1137/20M1374584]
Error Analysis for a Finite Difference Scheme for Axisymmetric Mean Curvature Flow of Genus-0 Surfaces
Nürnberg, Robert
2021-01-01
Abstract
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 onedimensional partial differential equation for a parameterization of the generating curve allows us to prove error bounds with respect to discrete L2 - and H1 -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 nonembedded self-shrinker for mean curvature flowFile | Dimensione | Formato | |
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