A multigrid preconditioner for stabilised discretisations of advection–diffusion problems

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.