Second Order in Time Finite Element Schemes for Curve Shortening Flow and Curve Diffusion
Abstract
Abstract. We prove optimal error bounds for a second order in time finite element approximation of curve shortening flow in possibly higher codimension. In addition, we introduce a second order in time method for curve diffusion. Both schemes are based on variational formulations of strictly parabolic systems of partial differential equations that feature a tangential velocity which under discretization is beneficial for the mesh quality. In each time step only two linear systems need to be solved. Numerical experiments demonstrate second order convergence as well as asymptotic equidistribution.
Fields of Study & Subjects
Advanced Numerical Methods in Computational Mathematics
Computational Fluid Dynamics and Aerodynamics
Rheology and Fluid Dynamics Studies
Publication details
- Journal / source
- SIAM Journal on Numerical Analysis
- Publisher
- Society for Industrial & Applied Mathematics (SIAM)
- Volume
- 64
- Issue
- 1
- Pages
- 103–124
- Publication date
- 28 January 2026
- Language
- EN