Moving mesh discontinuous galerkin method for hyperbolic conservation laws

Ruo Li*, Tao TANG

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

19 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)347-363
Number of pages17
JournalJournal of Scientific Computing
Volume27
Issue number1-3
DOIs
Publication statusPublished - Jun 2006

Scopus Subject Areas

  • Software
  • Theoretical Computer Science
  • Numerical Analysis
  • Engineering(all)
  • Computational Theory and Mathematics
  • Computational Mathematics
  • Applied Mathematics

User-Defined Keywords

  • Discontinuous Galerkin method
  • Monitor function
  • Moving mesh method
  • Nonlinear conservation laws

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