A finite element method for surface diffusion: the parametric case.
Surface diffusion is a geometry driven motion of a surface with normal velocity proportional to the surface Laplacian of mean curvature. It is described by a system of two second order nonlinear equations involving the Laplace-Beltrami operator. The system is discretized semi-implicitly in time. A system of linear elliptic partial differential equations needs to be solved at every time step. The spatial discretization uses continuous, piecewise polynomial finite elements. The solution of the resulting linear algebraic system is described in detail. The authors present possible obstacles when implementing the algorithm and show ways how to overcome them (mesh regularization, time-step control, mesh adaptation etc.). The exposition of the algorithm, supported by useful examples of computations, is clear, the results are convincing.
scientific article; zbMATH DE number 2132615