The contraction number of a multigrid method with mesh ratio 2 for solving Poisson's equation

AbstractThe convergence rate of a multigrid method for the solution of Poisson's equation on a uniform grid is estimated. In contrast to recent results of Braess, no intermediate grids are used. Refined estimates of Gauss-Seidel relaxation by weak norms, a strengthened Cauchy inequality, and a duality argument are central. We obtain 0.273 as an upper bound for the contraction number of the two-level procedure. The results hold for arbitrary convex polygonal regions and are independent of the smoothness of the solution