Local Discontinuous Galerkin Method for Surface Diffusion and Willmore Flow of Graphs |
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| Authors: | Yan Xu Chi-Wang Shu |
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| Affiliation: | 1. Department of Mathematics, University of Science and Technology of China, Hefei, Anhui, 230026, People’s Republic of China
2. Division of Applied Mathematics, Brown University, Providence, RI, 02912, USA
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| Abstract: | In this paper, we develop a local discontinuous Galerkin (LDG) finite element method for surface diffusion and Willmore flow of graphs. We prove L 2 stability for the equation of surface diffusion of graphs and energy stability for the equation of Willmore flow of graphs. We provide numerical simulation results for different types of solutions of these two types of the equations to illustrate the accuracy and capability of the LDG method. |
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