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 formulas. This numerical method admits a convergence analysis in the case of finite elements of polynomial degree at least 2 and backward difference formulas of orders 2 to 5. Numerical experiments in codimension 2 illustrate and complement our theoretical results.
1
TU Darmstadt, Germany
2
University of Regensburg, Germany
Tim Binz; Balázs Kovács. A convergent finite element algorithm for mean curvature flow in arbitrary codimension. Interfaces and free boundaries, Tome 25 (2023) no. 3, pp. 373-400. doi: 10.4171/ifb/493
@article{10_4171_ifb_493,
author = {Tim Binz and Bal\'azs Kov\'acs},
title = {A convergent finite element algorithm for mean curvature flow in arbitrary codimension},
journal = {Interfaces and free boundaries},
pages = {373--400},
year = {2023},
volume = {25},
number = {3},
doi = {10.4171/ifb/493},
url = {http://geodesic.mathdoc.fr/articles/10.4171/ifb/493/}
}
TY - JOUR
AU - Tim Binz
AU - Balázs Kovács
TI - A convergent finite element algorithm for mean curvature flow in arbitrary codimension
JO - Interfaces and free boundaries
PY - 2023
SP - 373
EP - 400
VL - 25
IS - 3
UR - http://geodesic.mathdoc.fr/articles/10.4171/ifb/493/
DO - 10.4171/ifb/493
ID - 10_4171_ifb_493
ER -
%0 Journal Article
%A Tim Binz
%A Balázs Kovács
%T A convergent finite element algorithm for mean curvature flow in arbitrary codimension
%J Interfaces and free boundaries
%D 2023
%P 373-400
%V 25
%N 3
%U http://geodesic.mathdoc.fr/articles/10.4171/ifb/493/
%R 10.4171/ifb/493
%F 10_4171_ifb_493
