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arXiv · 1911.05398

A finite element error analysis for axisymmetric mean curvature flow

John W. Barrett·Klaus Deckelnick·Robert Nürnberg
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Abstract

We consider the numerical approximation of axisymmetric mean curvature flow with the help of linear finite elements. In the case of a closed genus-1 surface, we derive optimal error bounds with respect to the $L^2$-- and $H^1$--norms for a fully discrete approximation. We perform convergence experiments to confirm the theoretical results, and also present numerical simulations for some genus-0 and genus-1 surfaces, including for the Angenent torus.

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John W. Barrett, Klaus Deckelnick, Robert Nürnberg. 2020-03-25. A finite element error analysis for axisymmetric mean curvature flow. https://doi.org/10.1093/imanum%2Fdraa020

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