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Moving Mesh Discontinuous Galerkin Method for Hyperbolic Conservation Laws

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Abstract

In this paper, a moving mesh discontinuous Galerkin (DG) method is developed to solve the nonlinear conservation laws. In the mesh adaptation part, two issues have received much attention. One is about the construction of the monitor function which is used to guide the mesh redistribution. In this study, a heuristic posteriori error estimator is used in constructing the monitor function. The second issue is concerned with the solution interpolation which is used to interpolates the numerical solution from the old mesh to the updated mesh. This is done by using a scheme that mimics the DG method for linear conservation laws. Appropriate limiters are used on seriously distorted meshes generated by the moving mesh approach to suppress the numerical oscillations. Numerical results are provided to show the efficiency of the proposed moving mesh DG method.

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Authors and Affiliations

  1. LMAM and School of Mathematical Sciences, Peking University, Peking, 100871, P.R. China

    Ruo Li

  2. Department of Mathematics, Hong Kong Baptist University, Kowloon Tong, Hong Kong

    Tao Tang

  3. Institute of Computational Mathematics, Chinese Academy of Sciences, Beijing, China

    Tao Tang

Authors
  1. Ruo Li
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  2. Tao Tang
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Correspondence to Ruo Li.

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Li, R., Tang, T. Moving Mesh Discontinuous Galerkin Method for Hyperbolic Conservation Laws. J Sci Comput 27, 347–363 (2006). https://doi.org/10.1007/s10915-005-9045-9

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  • DOI: https://doi.org/10.1007/s10915-005-9045-9

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