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arXiv · 2609.21871

A filtered time stepping scheme for curve shortening flow for open and closed curves

Klaus Deckelnick·Robert Nürnberg
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Abstract

We propose a filtered time stepping finite element scheme for curve shortening flow of open and closed curves in arbitrary codimension that is second-order accurate in time. Open curves are assumed to evolve inside a given domain $Ω\subset \mathbb R^n$, $n\geq2$, and meet the external boundary $\partialΩ$ orthogonally. We prove optimal error bounds for the $L^2$-- and $H^1$--norms. In practice only a single linear system needs to be solved at each time step. Numerical experiments confirm the accuracy and practicality of the introduced method, including an asymptotic equidistribution property.

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Klaus Deckelnick, Robert Nürnberg. 2026-09-18. A filtered time stepping scheme for curve shortening flow for open and closed curves. https://arxiv.org/abs/2609.21871

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