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

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.

Source: arXiv:2609.21871v1 - http://arxiv.org/abs/2609.21871v1 PDF: https://arxiv.org/pdf/2609.21871v1 Original Link: http://arxiv.org/abs/2609.21871v1