An Energy-Stable Minimal Deformation Rate Scheme for Mean Curvature Flow and Surface Diffusion
Abstract
Abstract. We propose a new parametric finite element method, referred to as the BGN-MDR method, for simulating both mean curvature flow and surface diffusion for closed hypersurfaces, as well as open hypersurfaces with moving contact lines in three dimensions. The method is also applicable to closed and open curves with moving contact points in two dimensions. The proposed scheme inherits the energy stability from the BGN scheme proposed by Barrett, Garcke, and Nürnberg in 2008 and offers improved mesh quality similar to the minimal deformation rate (MDR) method proposed by Hu and Li in 2022, especially for small time step sizes where the BGN scheme may become unstable and result in deteriorated meshes.
Fields of Study & Subjects
Advanced Numerical Methods in Computational Mathematics
Advanced Numerical Analysis Techniques
Advanced Mathematical Modeling in Engineering
Publication details
- Journal / source
- SIAM Journal on Scientific Computing
- Publisher
- Society for Industrial & Applied Mathematics (SIAM)
- Volume
- 48
- Issue
- 1
- Pages
- A103–A131
- Publication date
- 2 January 2026
- Language
- EN