An unconditionally stable finite element scheme for anisotropic curve shortening flow

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.

13 pages, 4 figures

References in corpus (2)

• Parametric finite element approximations of curvature driven interface evolutions
• Numerical approximation of curve evolutions in Riemannian manifolds

Cited by in corpus (1)

• Discrete anisotropic curve shortening flow in higher codimension