Garcke, Harald and Nuernberg, Robert (2021) Numerical approximation of boundary value problems for curvature flow and elastic flow in Riemannian manifolds. NUMERISCHE MATHEMATIK, 149 (2). pp. 375-415. ISSN 0029-599X, 0945-3245
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We present variational approximations of boundary value problems for curvature flow (curve shortening flow) and elastic flow (curve straightening flow) in two-dimensional Riemannian manifolds that are conformally flat. For the evolving open curves we propose natural boundary conditions that respect the appropriate gradient flow structure. Based on suitable weak formulations we introduce finite element approximations using piecewise linear elements. For some of the schemes a stability result can be shown. The derived schemes can be employed in very different contexts. For example, we apply the schemes to the Angenent metric in order to numerically compute rotationally symmetric self-shrinkers for the mean curvature flow. Furthermore, we utilise the schemes to compute geodesics that are relevant for optimal interface profiles in multi-component phase field models.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | WILLMORE FLOW; CURVES; SINGULARITIES; SURFACES; MOTION |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics > Prof. Dr. Harald Garcke |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 18 Aug 2022 09:03 |
| Last Modified: | 18 Aug 2022 09:03 |
| URI: | https://pred.uni-regensburg.de/id/eprint/46726 |
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