Elliott, Charles M. and Garcke, Harald and Kovacs, Balazs (2022) Numerical analysis for the interaction of mean curvature flow and diffusion on closed surfaces. NUMERISCHE MATHEMATIK, 151 (4). pp. 873-925. ISSN 0029-599X, 0945-3245
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An evolving surface finite element discretisation is analysed for the evolution of a closed two-dimensional surface governed by a system coupling a generalised forced mean curvature flow and a reaction-diffusion process on the surface, inspired by a gradient flow of a coupled energy. Two algorithms are proposed, both based on a system coupling the diffusion equation to evolution equations for geometric quantities in the velocity law for the surface. One of the numerical methods is proved to be convergent in the H-1 norm with optimal-order for finite elements of degree at least two. We present numerical experiments illustrating the convergence behaviour and demonstrating the qualitative properties of the flow: preservation of mean convexity, loss of convexity, weak maximum principles, and the occurrence of self-intersections.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | PARABOLIC DIFFERENTIAL-EQUATIONS; FINITE-ELEMENT METHODS; TIME DISCRETIZATION; EVOLVING SURFACE; CONVERGENCE; ALGORITHM; DRIVEN; PDES |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics > Prof. Dr. Harald Garcke |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 07 Feb 2024 10:07 |
| Last Modified: | 07 Feb 2024 10:07 |
| URI: | https://pred.uni-regensburg.de/id/eprint/57185 |
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