Year: 2026
Type: preprint
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.
Source: arXiv (Cornell University)
Authors: Deckelnick, Klaus, Nürnberg, Robert
Institutions: Otto-von-Guericke-Universität Magdeburg, University of Trento
Language: English
Subfield: Computational Mechanics
Field: Engineering
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7213906878