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Numerical analysis for the interaction of mean curvature flow and diffusion on closed surfaces
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Elliott, Charles M., Garcke, Harald and Kovács, Balázs (2022) Numerical analysis for the interaction of mean curvature flow and diffusion on closed surfaces. Numerische Mathematik, 151 . pp. 873-925. doi:10.1007/s00211-022-01301-3 ISSN 0029-599X.
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Official URL: https://doi.org/10.1007/s00211-022-01301-3
Abstract
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
| Item Type: | Journal Article | |||||||||
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| Subjects: | Q Science > QA Mathematics | |||||||||
| Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | |||||||||
| Library of Congress Subject Headings (LCSH): | Differential equations, Partial -- Numerical solutions, Geometric analysis, Manifolds (Mathematics), Surfaces | |||||||||
| Journal or Publication Title: | Numerische Mathematik | |||||||||
| Publisher: | Springer | |||||||||
| ISSN: | 0029-599X | |||||||||
| Official Date: | August 2022 | |||||||||
| Dates: |
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| Volume: | 151 | |||||||||
| Page Range: | pp. 873-925 | |||||||||
| DOI: | 10.1007/s00211-022-01301-3 | |||||||||
| Status: | Peer Reviewed | |||||||||
| Publication Status: | Published | |||||||||
| Access rights to Published version: | Open Access (Creative Commons) | |||||||||
| Date of first compliant deposit: | 20 June 2022 | |||||||||
| Date of first compliant Open Access: | 1 July 2022 | |||||||||
| RIOXX Funder/Project Grant: |
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