A moving mesh finite element algorithm for singular problems in two and three space dimensions

Ruo Li*, Tao TANG, Pingwen Zhang

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review

105 Citations (Scopus)


A framework for adaptive meshes based on the Hamilton-Schoen-Yau theory was proposed by Dvinsky. In a recent work (2001, J. Comput. Phys. 170, 562-588), we extended Dvinsky's method to provide an efficient moving mesh algorithm which compared favorably with the previously proposed schemes in terms of simplicity and reliability. In this work, we will further extend the moving mesh methods based on harmonic maps to deal with mesh adaptation in three space dimensions. In obtaining the variational mesh, we will solve an optimization problem with some appropriate constraints, which is in contrast to the traditional method of solving the Euler-Lagrange equation directly. The key idea of this approach is to update the interior and boundary grids simultaneously, rather than considering them separately. Application of the proposed moving mesh scheme is illustrated with some two- and three-dimensional problems with large solution gradients. The numerical experiments show that our methods can accurately resolve detail features of singular problems in 3D.

Original languageEnglish
Pages (from-to)365-393
Number of pages29
JournalJournal of Computational Physics
Issue number2
Publication statusPublished - 10 Apr 2002

Scopus Subject Areas

  • Numerical Analysis
  • Modelling and Simulation
  • Physics and Astronomy (miscellaneous)
  • Physics and Astronomy(all)
  • Computer Science Applications
  • Computational Mathematics
  • Applied Mathematics

User-Defined Keywords

  • Finite element method
  • Harmonic map
  • Moving mesh method
  • Optimization
  • Partial differential equations


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