V-cycle Galerkin-multigrid methods for nonconforming methods for nonsymmetric and indefinite problems Original Research Article

In this paper we analyze a class of View the MathML source-cycle multigrid methods for discretizations of second-order nonsymmetric and/or indefinite elliptic problems using nonconforming P1 and rotated Q1 finite elements. These multigrid 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. The analysis shows that these View the MathML source-cycle multigrid iterations with one smoothing on each level converge at a uniform rate provided that the coarsest level in the multilevel iterations is sufficiently fine (but independent of the number of multigrid levels). Various types of smoothers for the nonsymmetric and indefinite problems are considered and analyzed. The theory presented here also applies to mixed finite element methods for the nonsymmetric and indefinite problems.