Multigrid Algorithms for Nonconforming and Mixed Methods for Nonsymmetric and Indefinite Problems

In this paper we consider multigrid algorithms for nonconforming and mixed finite element methods for nonsymmetric and/or indefinite elliptic problems. We show that a simple V-cycle multigrid iteration using conforming coarse-grid corrections converges at a uniform rate provided that the coarsest level in the multilevel iteration is sufficiently fine (but independent of the number of multigrid levels). Various types of smoothers for the nonsymmetric and indefinite problems are discussed. Extensive numerical results are presented.