A Monotone, Second Order Accurate Scheme for Curvature Motion
Numerical Analysis
2022-12-12 v1 Numerical Analysis
Abstract
We present a second order accurate in time numerical scheme for curve shortening flow in the plane that is unconditionally monotone. It is a variant of threshold dynamics, a class of algorithms in the spirit of the level set method that represent interfaces implicitly. The novelty is monotonicity: it is possible to preserve the comparison principle of the exact evolution while achieving second order in time consistency. As a consequence of monotonicity, convergence to the viscosity solution of curve shortening is ensured by existing theory.
Keywords
Cite
@article{arxiv.2112.04693,
title = {A Monotone, Second Order Accurate Scheme for Curvature Motion},
author = {Selim Esedoglu and Jiajia Guo},
journal= {arXiv preprint arXiv:2112.04693},
year = {2022}
}