On a robust multigrid solver

Abstract

We consider a two-grid method based on approximation of the Schur complement. We study the dependence of the two-grid convergence rate on certain problem parameters. As test problems we take the rotated anisotropic diffusion equation and the convection-diffusion equation. Using Fourier analysis we show that for both test problems the two-grid method is robust w.r.t. variation in the relevant problem parameters. For the multigrid method we use a standardW-cycle on coarse grids. This multigrid method then has the same algorithmic structure as a standard multigrid method and is fairly efficient. Moreover, when applied to the two test problems then, as in the two-grid method, we have a strong robustness w.r.t. variation of the problem parameters.