Barrett, John W. and Garcke, Harald and Nurnberg, Robert (2008) A variational formulation of anisotropic geometric evolution equations in higher dimensions. NUMERISCHE MATHEMATIK, 109 (1). pp. 1-44. ISSN 0029-599X,
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We present a novel variational formulation of fully anisotropic motion by surface diffusion and mean curvature flow in R(d), d >= 2. This new formulation leads to an unconditionally stable, fully discrete, parametric finite element approximation in the case d = 2 or 3. The resulting scheme has very good properties with respect to the distribution of mesh points and, if applicable, volume conservation. This is demonstrated by several numerical experiments for d = 3, including regularized crystalline mean curvature flow and regularized crystalline surface diffusion.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | FINITE-ELEMENT-METHOD; SURFACE-DIFFUSION; FACETED SURFACES; CURVATURE; GROWTH; INTERFACE; MOTION; |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics > Prof. Dr. Harald Garcke |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 09 Nov 2020 07:55 |
| Last Modified: | 09 Nov 2020 07:55 |
| URI: | https://pred.uni-regensburg.de/id/eprint/31320 |
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