Local Discontinuous Galerkin Method for Surface Diffusion and Willmore Flow of Graphs

Authors:
Yan Xu;Chi-Wang Shu
Affiliations:
Department of Mathematics, University of Science and Technology of China, Anhui, People's Republic of China 230026;Division of Applied Mathematics, Brown University, Providence, USA 02912
Venue:
Journal of Scientific Computing
Year:
2009

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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.