Binz, Tim and Kovacs, Balazs (2023) A convergent finite element algorithm for mean curvature flow in arbitrary codimension. INTERFACES AND FREE BOUNDARIES, 25 (3). pp. 373-400. ISSN 1463-9963, 1463-9971
Full text not available from this repository. (Request a copy)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 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.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | CURVE SHORTENING FLOW; DIFFERENTIAL-EQUATIONS; GRADIENT FLOWS; SURFACES; APPROXIMATION; DIFFUSION; DRIVEN; SCHEME; . Mean curvature flow; higher codimension; evolving surface finite elements; backward difference formulas; error estimates |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 13 Mar 2024 14:31 |
| Last Modified: | 13 Mar 2024 14:31 |
| URI: | https://pred.uni-regensburg.de/id/eprint/59982 |
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