A L O C A L SMOOTING S T R A T E G Y MULTIGRID M E T H O D F OR STABILISED DISCRETISATIONS O F CONVECTION-DIFFUSION PROBLEMS

Abstract

In this paper, we discuss the development and practical application of multigrid methods with local smoothing to solve convection diffusion problems on adaptively refined meshes. The meshes are generated through adaptive refinement according to local error indicated by a residual-based a posteriori error estimation technique. We present a multigrid algorithm in which the smoothing is carried out only on the refined portion of the mesh. The smoothers, such as Gauss Seidel and ILU, give a good performance in both standard multigrid and local smoothing multigrid. Through several numerical examples, it seems that the rate of convergence of multigrid does not depend on the grid size and the viscosity parameter.