Barrett, John W. and Garcke, Harald and Nuernberg, Robert (2008) PARAMETRIC APPROXIMATION OF WILLMORE FLOW AND RELATED GEOMETRIC EVOLUTION EQUATIONS. SIAM JOURNAL ON SCIENTIFIC COMPUTING, 31 (1). pp. 225-253. ISSN 1064-8275,
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We present various variational approximations of Willmore flow in R-d, d - 2, 3. As well as the classic Willmore flow, we also consider variants that are (a) volume preserving and (b) volume and area preserving. The latter evolution law is the so-called Helfrich flow. In addition, we consider motion by Gauss curvature. The presented fully discrete schemes are easy to solve as they are linear at each time level, and they have good properties with respect to the distribution of mesh points. Finally, we present numerous numerical experiments, including simulations for energies appearing in the modeling of biological cell membranes.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | FINITE-ELEMENT-METHOD; GAUSS CURVATURE FLOW; FREE-BOUNDARY; SURFACE-DIFFUSION; FLAT SIDES; COMPUTATION; VESICLES; MOTION; HYPERSURFACES; EXISTENCE; Willmore flow; Helfrich flow; Gauss curvature; fourth order parabolic problem; parametric finite elements; tangential movement |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics > Prof. Dr. Harald Garcke |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 23 Nov 2020 11:23 |
| Last Modified: | 23 Nov 2020 11:23 |
| URI: | https://pred.uni-regensburg.de/id/eprint/31778 |
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