Barrett, John W. and Garcke, Harald and Nuernberg, Robert (2019) Variational discretization of axisymmetric curvature flows. NUMERISCHE MATHEMATIK, 141 (3). pp. 791-837. ISSN 0029-599X, 0945-3245
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We present natural axisymmetric variants of schemes for curvature flows introduced earlier by the present authors and analyze them in detail. Although numerical methods for geometric flows have been used frequently in axisymmetric settings, numerical analysis results so far are rare. In this paper, we present stability, equidistribution, existence and uniqueness results for the introduced approximations. Numerical computations show that these schemes are very efficient in computing numerical solutions of geometric flows as only a spatially one-dimensional problem has to be solved. The good mesh properties of the schemes also allow them to compute in very complex axisymmetric geometries.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | FINITE-ELEMENT APPROXIMATION; SURFACE-DIFFUSION; NUMERICAL SCHEME; PLANE-CURVES; EVOLUTION; HYPERSURFACES; STABILITY; DYNAMICS; DRIVEN; MOTION; |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics > Prof. Dr. Harald Garcke |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 21 Apr 2020 10:29 |
| Last Modified: | 21 Apr 2020 10:29 |
| URI: | https://pred.uni-regensburg.de/id/eprint/27499 |
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