Barrett, John W. and Garcke, Harald and Nuernberg, Robert (2007) On the variational approximation of combined second and fourth order geometric evolution equations. SIAM JOURNAL ON SCIENTIFIC COMPUTING, 29 (3). pp. 1006-1041. ISSN 1064-8275,
Full text not available from this repository. (Request a copy)Abstract
We present a variational formulation of combined motion by minus the Laplacian of curvature 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 or quadruple junction points or intersect the external boundary. On introducing a parametric finite element approximation, we prove stability bounds and compare our scheme with existing approaches. The presented scheme has very good properties with respect to the equidistribution of mesh points and, if applicable, area conservation.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | FINITE-ELEMENT-METHOD; MEAN-CURVATURE FLOW; LEVEL SET APPROACH; SURFACE-DIFFUSION; MULTIPLE JUNCTIONS; BOUNDARY MOTION; CURVES; COMPUTATION; STABILITY; ALLOYS; |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics > Prof. Dr. Harald Garcke |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 14 Jan 2021 07:28 |
| Last Modified: | 14 Jan 2021 07:28 |
| URI: | https://pred.uni-regensburg.de/id/eprint/33603 |
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