Garcke, Harald and Nürnberg, Robert (2021) Structure-preserving discretizations of gradient flows for axisymmetric two-phase biomembranes. IMA JOURNAL OF NUMERICAL ANALYSIS, 41 (3). pp. 1899-1940. ISSN 0272-4979, 1464-3642
Full text not available from this repository. (Request a copy)Abstract
The form and evolution of multi-phase biomembranes are of fundamental importance in order to understand living systems. In order to describe these membranes, we consider a mathematical model based on a Canham-Helfrich-Evans two-phase elastic energy, which will lead to fourth-order geometric evolution problems involving highly nonlinear boundary conditions. We develop a parametric finite element method in an axisymmetric setting. Using a variational approach it is possible to derive weak formulations for the highly nonlinear boundary value problems such that energy decay laws, as well as conservation properties, hold for spatially discretized problems. We will prove these properties and show that the fully discretized schemes are well posed. Finally, several numerical computations demonstrate that the numerical method can be used to compute complex, experimentally observed two-phase biomembranes.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | CURVATURE; APPROXIMATION; MEMBRANES; ELASTICITY; VESICLES; SHAPE; biomembranes; multi-phase Canham-Helfrich-Evans energy; Willmore flow; parametric finite elements; stability; numerical simulations |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics > Prof. Dr. Harald Garcke |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 05 Jul 2022 06:25 |
| Last Modified: | 05 Jul 2022 06:25 |
| URI: | https://pred.uni-regensburg.de/id/eprint/46872 |
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