Discrete duality finite volume method for mean curvature flow of surfaces

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Lukáš Tomek Karol Mikula Mariana Remešíková


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. 

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Tomek, L., Mikula, K., & Remešíková, M. (2016). Discrete duality finite volume method for mean curvature flow of surfaces. Proceedings Of The Conference Algoritmy, , 33-43. Retrieved from http://www.iam.fmph.uniba.sk/amuc/ojs/index.php/algoritmy/article/view/392/309


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