Barrett, John W. and Garcke, Harald and Nuernberg, Robert (2008) Numerical approximation of anisotropic geometric evolution equations in the plane. IMA JOURNAL OF NUMERICAL ANALYSIS, 28 (2). pp. 292-330. ISSN 0272-4979,
Full text not available from this repository.Abstract
We present a variational formulation of fully anisotropic motion by surface diffusion and mean curvature flow, as well as related flows. The proposed scheme covers both the closed-curve case and the case of curves that are connected via triple junction points. On introducing a parametric finite-element approximation, we prove stability bounds and report on numerical experiments, including regularized crystalline mean curvature flow and regularized crystalline surface diffusion. The presented scheme has very good properties with respect to the distribution of mesh points and, if applicable, area conservation.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | MEAN-CURVATURE FLOW; FINITE-ELEMENT-METHOD; CURVE SHORTENING FLOW; SURFACE-DIFFUSION; DISCRETE SCHEME; DOUBLE BUBBLE; MOTION; INTERFACE; BOUNDARY; GROWTH; anisotropic surface diffusion; anisotropic mean curvature flow; crystalline surface energy; triple junctions; parametric finite elements; Schur complement; tangential movement |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics > Prof. Dr. Harald Garcke |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 04 Nov 2020 11:28 |
| Last Modified: | 04 Nov 2020 11:28 |
| URI: | https://pred.uni-regensburg.de/id/eprint/31097 |
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