Moving Mesh Methods in Multiple Dimensions Based on Harmonic Maps

@inproceedings{Li2000MovingMM,
  title={Moving Mesh Methods in Multiple Dimensions Based on Harmonic Maps},
  author={Ruo Li and Tao Tang and Pingwen Zhang},
  year={2000}
}
In practice, there are three types of adaptive methods using the finite element approach, namely the h-method,p-method, andr-method. In theh-method, the overall method contains two parts, a solution algorithm and a mesh selection algorithm. These two parts are independent of each other in the sense that the change of the PDEs will affect the first part only. However, in some of the existing versions of the r-m thod (also known as themoving mesh method ), these two parts are strongly associated… CONTINUE READING
Highly Influential
This paper has highly influenced 10 other papers. REVIEW HIGHLY INFLUENTIAL CITATIONS
Highly Cited
This paper has 284 citations. REVIEW CITATIONS

From This Paper

Figures, tables, and topics from this paper.

Citations

Publications citing this paper.
Showing 1-10 of 100 citations

284 Citations

02040'01'04'08'12'16
Citations per Year
Semantic Scholar estimates that this publication has 284 citations based on the available data.

See our FAQ for additional information.

References

Publications referenced by this paper.
Showing 1-10 of 35 references

Spectral methods for singular perturbation problems, in Proceedings of Symposia in Applied Mathematics

  • W.-B. Liu, T. Tang
  • edited by W. Gautschi (Amer. Math. Soc…
  • 1994
Highly Influential
5 Excerpts

Adaptive zoning for singular problems in two dimensions

  • J. U. Brackbill, J. S. Saltzman
  • J. Comput. Phys. 46,
  • 1982
Highly Influential
8 Excerpts

Numerical solution of the quasi-linear Poisson equation in a nonuniform triangle mesh

  • A. Winslow
  • J. Comput. Phys.1,
  • 1967
Highly Influential
9 Excerpts

An r-adaptive finite element method based upon moving mesh PDEs,J

  • W. M. Cao, W. Z. Huang, R. D. Russell
  • Comput. Phys. 149,
  • 1999
Highly Influential
8 Excerpts

An adaptive grid with direction control

  • J. U. Brackbill
  • J. Comput. Phys. 108,
  • 1993
Highly Influential
8 Excerpts

Dvinsky, Adaptive grid generation from harmonic maps on Riemannian manifolds

  • A S.
  • J. Comput. Phys. 95,
  • 1991
Highly Influential
4 Excerpts

An adaptive finite element method for initial–boundary value problems for partial differential equations

  • S. F. Davis, J. E. Flaherty
  • SIAM J. Sci. Stat
  • 1982
Highly Influential
5 Excerpts

On univalent harmonic maps between surfaces, Invent

  • R. Schoen, S.-T. Yau
  • 1978
Highly Influential
7 Excerpts

Maps of Manifolds with Boundary

  • R. Hamilton, Harmonic
  • Lecture Notes in Mathematics (Springer-Verlag…
  • 1975
Highly Influential
8 Excerpts