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arXiv · 2310.02138

Discrete anisotropic curve shortening flow in higher codimension

Klaus Deckelnick·Robert Nürnberg
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Abstract

We introduce a novel formulation for the evolution of parametric curves by anisotropic curve shortening flow in ${\mathbb R}^d$, $d\geq2$. The reformulation hinges on a suitable manipulation of the parameterization's tangential velocity, leading to a strictly parabolic differential equation. Moreover, the derived equation is in divergence form, giving rise to a natural variational numerical method. For a fully discrete finite element approximation based on piecewise linear elements we prove optimal error estimates. Numerical simulations confirm the theoretical results and demonstrate the practicality of the method.

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Klaus Deckelnick, Robert Nürnberg. 2023-10-03. Discrete anisotropic curve shortening flow in higher codimension. https://doi.org/10.1093/imanum%2Fdrae015

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