A convergent finite element algorithm for mean curvature flow in arbitrary codimension

2021/07/22 by Tim Binz, Balázs Kovács, Binz, Tim +1 · 1 citation
Engineering · Mathematics · #35R01 #53E10 #65M12 #65M15 #65M60 #Advanced Numerical Analysis Techniques #Advanced Numerical Methods in Computational Mathematics #Differential Equations and Numerical Methods #FOS: Mathematics #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.2107.10577

openalex publication_date 2021/07/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Optimal-order uniform-in-time H¹-norm error estimates are given for semi- and full discretizations of mean curvature flow of surfaces in arbitrarily high codimension. The proposed and studied numerical method is based on a parabolic system coupling the surface flow to evolution equations for the mean curvature vector and for the orthogonal projection onto the tangent space. The algorithm uses evolving surface finite elements and linearly implicit backward difference formulae. This numerical method admits a convergence analysis in the case of finite elements of polynomial degree at least two and backward difference formulae of orders two to five. Numerical experiments in codimension 2 illustrate and complement our theoretical results.

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• Error estimates for a surface finite element method for anisotropic mean curvature flow

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