Barrett, John W. and Garcke, Harald and Nuernberg, Robert (2010) Parametric approximation of surface clusters driven by isotropic and anisotropic surface energies. INTERFACES AND FREE BOUNDARIES, 12 (2). pp. 187-234. ISSN 1463-9963,
Full text not available from this repository. (Request a copy)Abstract
We present a variational formulation for the evolution of surface clusters in R 3 by mean curvature flow, surface diffusion and their anisotropic variants. We introduce the triple junction line conditions that are induced by the considered gradient flows, and present weak formulations of these flows. In addition, we consider the case where a subset of the boundaries of these clusters are constrained to lie on an external boundary. These formulations lead to unconditionally stable, fully discrete, parametric finite element approximations. The resulting schemes have very good properties with respect to the distribution of mesh points and, if applicable, volume conservation. This is demonstrated by several numerical experiments, including isotropic double, triple and quadruple bubbles, as well as clusters evolving under anisotropic mean curvature flow and anisotropic surface diffusion, including computations for regularized crystalline surface energy densities.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | GEOMETRIC EVOLUTION-EQUATIONS; MEAN-CURVATURE; SOAP-BUBBLE; NUMERICAL SIMULATIONS; BOUNDARY MOTION; GRAIN-GROWTH; INTERFACE; FILMS; FLOW; DIFFUSION; Surface cluster; mean curvature flow; surface diffusion; soap bubbles; triple junction lines; parametric finite elements; anisotropy; tangential movement |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics > Prof. Dr. Harald Garcke |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 17 Aug 2020 09:00 |
| Last Modified: | 17 Aug 2020 09:00 |
| URI: | https://pred.uni-regensburg.de/id/eprint/25482 |
Actions (login required)
 |
View Item |
