Barrett, John W. and Garcke, Harald and Nurnberg, Robert (2017) Stable variational approximations of boundary value problems for Willmore flow with Gaussian curvature. IMA JOURNAL OF NUMERICAL ANALYSIS, 37 (4). pp. 1657-1709. ISSN 0272-4979, 1464-3642
Full text not available from this repository. (Request a copy)Abstract
We study numerical approximations for geometric evolution equations arising as gradient flows for energy functionals that are quadratic in the principal curvatures of a two-dimensional surface. Besides the well-known Willmore and Helfrich flows, we will also consider flows involving the Gaussian curvature of the surface. Boundary conditions for these flows are highly nonlinear, and we use a variational approach to derive weak formulations, which naturally can be discretized with the help of a mixed finite element method. Our approach uses a parametric finite element method, which can be shown to lead to good mesh properties. We prove stability estimates for a semidiscrete (discrete in space, continuous in time) version of the method and show existence and uniqueness results in the fully discrete case. Finally, several numerical results are presented involving convergence tests, as well as the first computations with Gaussian curvature and/or free or semifree boundary conditions.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | GEOMETRIC EVOLUTION-EQUATIONS; FINITE-ELEMENT-METHOD; FLUID MEMBRANES; LIPID-MEMBRANES; MEAN-CURVATURE; SURFACES; COMPUTATION; ALGORITHM; VESICLES; Willmore flow; parametric finite elements; tangential movement; spontaneous curvature; 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: | 14 Dec 2018 13:19 |
| Last Modified: | 21 Feb 2019 13:02 |
| URI: | https://pred.uni-regensburg.de/id/eprint/2083 |
Actions (login required)
 |
View Item |
