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

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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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Authors and Affiliations

  1. Department of Mathematics, University of Science and Technology of China, Hefei, Anhui, 230026, People’s Republic of China

    Yan Xu

  2. Division of Applied Mathematics, Brown University, Providence, RI, 02912, USA

    Chi-Wang Shu

Authors
  1. Yan Xu
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  2. Chi-Wang Shu
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Correspondence to Yan Xu.

Additional information

Y. Xu research supported by NSFC grant 10601055 and Foundation for Authors of Excellent Doctoral Dissertations of the Chinese Academy of Sciences.

C.-W. Shu research supported in part by NSFC grant 10671190 during his visit to the Department of Mathematics, University of Science and Technology of China, Hefei, Anhui 230026, P.R. China. Additional support is provided by NSF grants DMS-0510345 and DMS-0809086 and by DOE grant DE-FG02-08ER25863.

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Xu, Y., Shu, CW. Local Discontinuous Galerkin Method for Surface Diffusion and Willmore Flow of Graphs. J Sci Comput 40, 375–390 (2009). https://doi.org/10.1007/s10915-008-9262-0

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  • DOI: https://doi.org/10.1007/s10915-008-9262-0

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