Anisotropic mean curvature flow for two-dimensional surfaces in higher codimension: A numerical scheme
The aim of the paper is to derive numerical schemes for the mean curvature flow for two-dimensional surfaces in higher codimension. Since the chosen numerical method is that of finite elements the author needs the weak formulation too. She proves that the numerical method is stable, and numerical simulation illustrates the efficiency of the method. After an introductory section, the author gives in Section 2 a proper definition of the energy functional. In section 3 a brief review of the concepts which helps the reader to gain a geometric intuition are presented. The next section presents the definition of the of the mean curvature vector \(H_{F}\) and that of anisotropic curvature flow. The weak formulation of the flow is given in Section 5. Section 6 is devoted to the the finite element method (FEM) and two FEM schemes are presented. In Section 8 numerical and graphical examples are considered. Finally, Section 9 contains a generalization of Wulff shapes for higher codimension.
scientific article; zbMATH DE number 5500719