Numerical solution for the Willmore flow of graphs. (English) Zbl 1145.65323

Oberhuber, Tomáš

Beneš, Michal (ed.) et al., Proceedings of Czech-Japanese Seminar in Applied Mathematics 2005, Kuju, Japan, September 15–18, 2005. Fukuoka: Kyushu University, The 21st Century COE Program “DMHF”. COE Lecture Note 3, 126-138 (2006).

Summary: In this article we present a numerical scheme for the Willmore flow of graphs. It is based on the method of lines. Resulting ordinary differential equations are solved using the fourth-order Runge-Kutta-Merson solver. We show basic properties of the semi-discrete scheme and present several computational studies of evolving graphs.
For the entire collection see [Zbl 1141.65001].

MSC:

65M60	Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
35K55	Nonlinear parabolic equations
35K35	Initial-boundary value problems for higher-order parabolic equations
53C44	Geometric evolution equations (mean curvature flow, Ricci flow, etc.) (MSC2010)
74H15	Numerical approximation of solutions of dynamical problems in solid mechanics