A multigrid preconditioner for stabilised discretisations of advection-diffusion problems

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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

Keywords

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

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