Barrett, John W. and Garcke, Harald and Nuernberg, Robert (2007) A parametric finite element method for fourth order geometric evolution equations. JOURNAL OF COMPUTATIONAL PHYSICS, 222 (1). pp. 441-467. ISSN 0021-9991,
Full text not available from this repository. (Request a copy)Abstract
We present a finite element approximation of motion by minus the Laplacian of curvature and related flows. The proposed scheme covers both the closed curve case, and the case of curves that are connected via triple junctions. On introducing a parametric finite element approximation, we prove stability bounds and compare our scheme with existing approaches. It turns out that the new scheme has very good properties with respect to area conservation and the equidistribution of mesh points. We state also an extension of our scheme to Willmore flow of curves and discuss possible further generalizations. (c) 2006 Elsevier Inc. All rights reserved.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | MEAN-CURVATURE FLOW; LEVEL SET APPROACH; SURFACE-DIFFUSION; ERROR ANALYSIS; MOTION; FILMS; ELECTROMIGRATION; APPROXIMATION; COMPUTATION; FORMULATION; surface diffusion; Willmore flow; triple junctions; fourth order parabolic problem; 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: | 22 Dec 2020 07:07 |
| Last Modified: | 22 Dec 2020 07:07 |
| URI: | https://pred.uni-regensburg.de/id/eprint/33111 |
Actions (login required)
 |
View Item |
