PreprintCC BY-NC-ND 4.0arXiv
A filtered time stepping scheme for curve shortening flow for open and closed curves
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⊂ ℝn, n≥2, and meet the external boundary ∂Ω orthogonally. We prove optimal error bounds for the L2-- and H1--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.
Related
- A Second-Order Semi-Implicit Projection Time-Stepping Scheme for the Shallow-Water Equations on the Sphere Using Compatible Finite Elements
- Multi-time-stepping splitting scheme with mass lumping for the multiscale wave equation
- Tangential stability and fully discrete convergence of the classical BGN scheme for curve shortening flow
- On hyperbolic PDEs, filtered feedback control laws, and fractal-like stability crossing curves
- Towards Digital Halftoning on Closed Manifolds--An Error Diffusion Scheme for the 2D Torus based on Sigma-Delta Quantization along the Rank-one Lattice
BibTeX
@misc{deckelnick2026filtered,
title = {{A filtered time stepping scheme for curve shortening flow for open and closed curves}},
author = {Klaus Deckelnick and Robert Nürnberg},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.21871},
eprint = {2609.21871},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.21871},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - A filtered time stepping scheme for curve shortening flow for open and closed curves
AU - Klaus Deckelnick
AU - Robert Nürnberg
PY - 2026
DA - 2026/09/18
PB - arXiv
DO - 10.48550/arxiv.2609.21871
UR - https://arxiv.org/abs/2609.21871
AB - 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⊂ ℝ^n, n≥2, and meet the external boundary ∂Ω 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.
ER -