An unconditionally stable finite element scheme for anisotropic curve shortening flow

TL;DR

This paper introduces a fully discrete finite element scheme for anisotropic curve shortening flow, proving its stability and uniqueness, and validating it through numerical experiments.

Contribution

It presents a novel finite element method for anisotropic curve shortening flow with proven stability and existence results, advancing numerical analysis in geometric evolution equations.

Findings

The scheme is unconditionally stable.

Existence and uniqueness of solutions are established.

Numerical results confirm theoretical stability and practicality.

Abstract

Based on a recent novel formulation of parametric anisotropic curve shortening flow, we analyse a fully discrete numerical method of this geometric evolution equation. The method uses piecewise linear finite elements in space and a backward Euler approximation in time. We establish existence and uniqueness of a discrete solution, as well as an unconditional stability property. Some numerical computations confirm the theoretical results and demonstrate the practicality of our method.