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Numerical Analysis Seminar
Seminar information archive ～04/23｜Next seminar｜Future seminars 04/24～
| Date, time & place | Tuesday 16:30 - 18:00 002Room #002 (Graduate School of Math. Sci. Bldg.) |
|---|---|
| Organizer(s) | Norikazu Saito, Takahito Kashiwabara |
2020/10/27
16:30-18:00 Online
Buyang Li (The Hong Kong Polytechnic University)
Convergent evolving finite element algorithms for mean curvature flow and Willmore flow of closed surfaces (English)
https://forms.gle/HeuUxWLGa696KPvz8
Buyang Li (The Hong Kong Polytechnic University)
Convergent evolving finite element algorithms for mean curvature flow and Willmore flow of closed surfaces (English)
[ Abstract ]
We construct evolving surface finite element methods for the mean curvature and Willmore flow through equivalently reformulating the original equations into coupled systems governing the evolution of surface position, velocity, normal vector and mean curvature. Then we prove $H^1$-norm convergence of the proposed evolving surface finite element methods for the reformulated systems, by combining stability estimates and consistency estimates. The stability analysis is based on the matrix–vector formulation of the finite element method and does not use geometric arguments. The geometry enters only into the consistency estimates. Numerical experiments illustrate and complement the theoretical results.
[1] https://doi.org/10.1007/s00211-019-01074-2
[2] https://arxiv.org/abs/2007.15257
[ Reference URL ]We construct evolving surface finite element methods for the mean curvature and Willmore flow through equivalently reformulating the original equations into coupled systems governing the evolution of surface position, velocity, normal vector and mean curvature. Then we prove $H^1$-norm convergence of the proposed evolving surface finite element methods for the reformulated systems, by combining stability estimates and consistency estimates. The stability analysis is based on the matrix–vector formulation of the finite element method and does not use geometric arguments. The geometry enters only into the consistency estimates. Numerical experiments illustrate and complement the theoretical results.
[1] https://doi.org/10.1007/s00211-019-01074-2
[2] https://arxiv.org/abs/2007.15257
https://forms.gle/HeuUxWLGa696KPvz8
