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.
- streamline upwinding