A finite element error analysis for axisymmetric mean curvature flow

Abstract

We consider the numerical approximation of axisymmetric mean curvature flow with the help of linear finite elements. In the case of a closed genus-1 surface, we derive optimal error bounds with respect to the $L^2$-- and $H^1$--norms for a fully discrete approximation. We perform convergence experiments to confirm the theoretical results, and also present numerical simulations for some genus-0 and genus-1 surfaces, including for the Angenent torus.

24 pages, 10 figures

References in corpus (4)

• Parametric finite element approximations of curvature driven interface evolutions
• Finite element methods for fourth order axisymmetric geometric evolution equations
• Variational discretization of axisymmetric curvature flows
• The entropy of the Angenent torus is approximately 1.85122

Cited by in corpus (5)

• A novel finite element approximation of anisotropic curve shortening flow
• Numerical approximation of boundary value problems for curvature flow and elastic flow in Riemannian manifolds
• Convergence of Dziuk's semidiscrete finite element method for mean curvature flow of closed surfaces with high-order finite elements
• On the numerical approximation of hyperbolic mean curvature flows for surfaces
• Error analysis for a finite difference scheme for axisymmetric mean curvature flow of genus-0 surfaces