Discrete duality finite volume method for mean curvature flow of surfaces - Tomek, Lukáš; Mikula, Karol; Remešíková, Mariana (Proceedings of the Conference Algoritmy, 2016)
In this paper we propose a new numerical method for solving the mean curvature flow of surfaces. Two-dimensional surface is usualy approximated by a triangular mesh. Widely used discretization of Laplace-Beltrami operator over triangulated surfaces is the so-called cotangent scheme [7,8]. In the cotangent scheme the unknowns are the vertices of the triangulation. The basic idea of our new approach is to include a representative point of each triangle (vertex of the dual mesh) in the scheme as a supplementary unknown and generalize the discrete duality finite volume method [3] from~$R^2$ to 2D~surfacesembedded in~$R^3$. We derive the numerical scheme and present numerical experiments illustrating the basic properties of the meth od.