Barrett, John W. and Garcke, Harald and Nürnberg, Robert (2021) Stable approximations for axisymmetric Willmore flow for closed and open surfaces. ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE, 55 (3). pp. 833-885. ISSN 0764-583X, 1290-3841
Full text not available from this repository. (Request a copy)Abstract
For a hypersurface in Double-struck capital R-3, Willmore flow is defined as the L-2-gradient flow of the classical Willmore energy: the integral of the squared mean curvature. This geometric evolution law is of interest in differential geometry, image reconstruction and mathematical biology. In this paper, we propose novel numerical approximations for the Willmore flow of axisymmetric hypersurfaces. For the semidiscrete continuous-in-time variants we prove a stability result. We consider both closed surfaces, and surfaces with a boundary. In the latter case, we carefully derive weak formulations of suitable boundary conditions. Furthermore, we consider many generalizations of the classical Willmore energy, particularly those that play a role in the study of biomembranes. In the generalized models we include spontaneous curvature and area difference elasticity (ADE) effects, Gaussian curvature and line energy contributions. Several numerical experiments demonstrate the efficiency and robustness of our developed numerical methods.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | FINITE-ELEMENT-METHOD; ELASTIC FLOW; PARAMETRIC APPROXIMATION; SPONTANEOUS CURVATURE; SHAPE; MEMBRANES; ALGORITHM; VESICLES; Willmore flow; Helfrich flow; axisymmetry; parametric finite elements; stability; tangential movement; spontaneous curvature; ADE model; clamped boundary conditions; Navier boundary conditions; Gaussian curvature energy; line energy |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics > Prof. Dr. Harald Garcke |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 25 Aug 2022 05:18 |
| Last Modified: | 25 Aug 2022 05:18 |
| URI: | https://pred.uni-regensburg.de/id/eprint/46926 |
Actions (login required)
 |
View Item |
