On tangential stabilization in curvature driven flows of planar curves

TL;DR

This paper investigates how tangential stabilization influences curvature-driven flows of planar curves, focusing on numerical stability and uniform point redistribution to prevent instabilities during evolution.

Contribution

It introduces a tangential velocity functional that ensures uniform grid point distribution, enhancing numerical stability in curvature-driven flow simulations.

Findings

Tangential stabilization prevents numerical instabilities.

Uniform redistribution of grid points is achieved.

The method improves the robustness of curvature flow computations.

Abstract

We discuss the role of tangential stabilization in a curvature driven flow of planar curves. The governing system of nonlinear parabolic equations includes a nontrivial tangential velocity functional yielding a uniform redistribution of grid points along the evolving family of curves preventing numerically computed curves from forming various instabilities.