THE HIERARCHICAL BASIS MULTIGRID METHOD FOR CONVECTION DIFFUSION-EQUATIONS

We make a theoretical study of the application of a standard hierarchical basis multigrid iteration to the convection diffusion equation, discretized using an upwind finite element discretizations. We show behavior that in some respects is similar to the symmetric positive definite case, but in other respects is markedly different. In particular, we find the rate of convergence depends significantly on parameters which measure the strength of the upwinding. and the size of the convection term. Numerical calculations illustrating some of these effects are given.