V-CYCLE GALERKIN-MULTIGRID METHODS FOR NONCONFORMING METHODS FOR NONSYMMETRIC AND INDEFINITE PROBLEMS

In this paper we analyze a class of V-cycle multigrid methods for disc retizations of second-order nonsymmetric and/or indefinite elliptic pr oblems using nonconforming Pt and rotated el finite elements. These mu ltigrid methods are based on the so-called Galerkin approach where the quadratic forms over coarse grids are constructed from the quadratic form on the finest grid and iterated coarse-to-fine grid operators. Th e analysis shows that these V-cycle multigrid iterations with one smoo thing on each level converge at a uniform rate provided that the coars est level in the multilevel iterations is sufficiently fine (but indep endent of the number of multigrid levels). Various types of smoothers for the nonsymmetric and indefinite problems are considered and analyz ed. The theory presented here also applies to mixed finite element met hods for the nonsymmetric and indefinite problems. (C) 1998 Elsevier S cience B.V. and IMACS. All rights reserved.