Uniform Convergence of Multigrid V{cycle Iterations for Indefinite and Nonsymmetric Problems

In this paper, we present an analysis of a multigrid method for nonsym-metric and/or indeenite elliptic problems. In this multigrid method various types of smoothers may be used. One type of smoother which we consider is deened in terms of an associated symmetric problem and includes point and line, Jacobi and Gauss-Seidel iterations. We also study smoothers based entirely on the original operator. One is based on the normal form, that is, the product of the operator and its transpose. Other smoothers studied include point and line, Jacobi and Gauss-Seidel (with certain orderings). We show that the uniform estimates of 6] for symmetric positive deenite problems carry over to these algorithms. More precisely, the multigrid iteration for the nonsymmetric and/or indeenite problem is shown to converge at a uniform rate provided that the coarsest grid in the multilevel iteration is suuciently ne (but not depending on the number of multigrid levels).