Multigrid convergence for nonsymmetric, indefinite variational problems and one smoothing step

Abstract

We prove that the multigrid method for linear systems arising from nonsymmetric and indefinite elliptic variational problems converges for all sufficiently small h with one smoothing step only. Previous proofs required that the number of smoothing steps be within certain bounds, which were quite difficult to compute. Our theory is based on sharp energy norm convergence estimates for the symmetric, definite case, and lower order terms are treated as perturbations. The resulting estimates are so sharp that we obtain even the convergence of the V-cycle.