A multigrid preconditioner for stabilised discretisations of advection-diffusion problems

Research output: Contribution to journalArticle

29 Citations (Scopus)

Abstract

This paper is concerned with the iterative solution of linear systems arising from stabilised discretisations of advection-diffusion problems on stretched finite element grids. Using nonuniform grids of this type leads, in general, to very badly conditioned matrix problems. We therefore consider using GMRES in conjunction with a multigrid (MG) preconditioning strategy. In particular, we show that in order to achieve the grid-size independent convergence which is characteristic of MG methods, it is essential to use an effective stabilisation strategy at each level of the MG structure.

Original languageEnglish
Pages (from-to)187-203
Number of pages17
JournalJournal of Computational and Applied Mathematics
Volume110
Issue number1
DOIs
Publication statusPublished - 15 Oct 1999

Fingerprint

Advection-diffusion
Diffusion Problem
Advection
Preconditioner
Linear systems
Stabilization
Discretization
Grid
Non-uniform Grid
GMRES
Multigrid Method
Iterative Solution
Preconditioning
Linear Systems
Finite Element
Strategy

Keywords

  • advection-diffusion
  • GMRES
  • multigrid
  • stabilisation
  • streamline upwinding

Cite this

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A multigrid preconditioner for stabilised discretisations of advection-diffusion problems. / Ramage, A.

In: Journal of Computational and Applied Mathematics, Vol. 110, No. 1, 15.10.1999, p. 187-203.

Research output: Contribution to journalArticle

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