Moving Mesh Methods for Problems with Blow-Up

  title={Moving Mesh Methods for Problems with Blow-Up},
  author={Chris J. Budd and Weizhang Huang and Robert D. Russell},
  journal={SIAM J. Scientific Computing},
Abstract. In this paper we consider the numerical solution of PDEs with blow-up for which scaling invariance plays a natural role in describing the underlying solution structures. It is a challenging numerical problem to capture the qualitative behaviour in the blow-up region, and the use ofnonuniform meshes is essential. We consider moving mesh methods for which the mesh is determined using so-called moving mesh partial differential equations (MMPDEs). Specifically, the underlying PDE and the… CONTINUE READING

From This Paper

Topics from this paper.


Publications citing this paper.
Showing 1-10 of 73 extracted citations


Publications referenced by this paper.
Showing 1-9 of 9 references

Moving mesh methods based upon moving meshpartial di erential equations

  • Y. Ren Huang
  • SIAM J . Numer . Anal .
  • 1994

Dynamic rezone methods for partial di erential equationsin one space dimension

  • B. Larrouturou
  • Ann . Inst . H . Poincar
  • 1993

Self - similar solutions of a quasilineardi usion problem

  • J. W. Dold, A. M. Stuart
  • SIAM J . Anal .
  • 1993

Final time blowup pro les for semilinear parabolic equations viacentre manifold theory

  • V. A. Galaktionov
  • SIAM J . Appl . Math .
  • 1992

PETZOLD, A description

  • L R.
  • Phys. Rev. A,
  • 1986

A numerical study of three moving gridmethods for one - dimensional partial di erential equations which are based on the methodof lines

  • J. G. Verwer, P. A. Zegeling
  • Indiana Univ . Math . J .
  • 1985

Asymptotically self-similar blowup ofsemilinear heat equations, Comm

  • R. KOHN
  • Pure Appl. Math.,
  • 1985

Simple adaptive grids for 1 - D initial value problems

  • L. O'c. Drury
  • Comm . Pure Appl . Math .
  • 1981

The focusing singularity ofthe nonlinear Schr  odinger equation

  • C. Sulem
  • Quart . J . Mech . Appl . Math .
  • 1977

Similar Papers

Loading similar papers…