Garcke, Harald and Nürnberg, Robert and Zhao, Quan (2025) Stable fully discrete finite element methods with BGN tangential motion for Willmore flow of planar curves. JOURNAL OF SCIENTIFIC COMPUTING, 105 (2): 45. ISSN 0885-7474, 1573-7691
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We propose and analyze stable finite element approximations for Willmore flow of planar curves. The presented schemes are based on a novel weak formulation which combines an evolution equation for curvature with the curvature formulation originally proposed by Barrett, Garcke and N & uuml;rnberg (BGN) in (Barrett et al. in J. Comput. Phys. 222:441-467, 2007). Under discretization in space with piecewise linear elements this leads to a stable continuous-in-time semidiscrete scheme, which retains the equidistribution property from the BGN methods. Furthermore, two fully discrete schemes can be shown to satisfy unconditional energy stability estimates. Numerical examples are presented to showcase the good properties of the introduced schemes, including an asymptotic equidistribution of vertices.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | ELASTIC FLOW; PARAMETRIC APPROXIMATION; TIME DISCRETIZATION; EVOLUTION; ENERGY; Willmore flow; Planar curves; Finite element method; Energy stability; Equidistribution |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics > Prof. Dr. Harald Garcke |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 18 Jun 2026 08:23 |
| Last Modified: | 18 Jun 2026 08:23 |
| URI: | https://pred.uni-regensburg.de/id/eprint/66967 |
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