CONVERGENCE OF NONCONFORMING OR NONNESTED MULTIGRID METHODS WITHOUT FULL
                             ELLIPTIC REGULARITY

                              Susanne C. Brenner

                          Department of Mathematics
                        University of South Carolina 
                              Columbia, SC 29208
                          brenner@math.scarolina.edu

Abstract.  We consider nonconforming or nonnested multigrid methods for second
and fourth order elliptic boundary value problems which do not have full
elliptic regularity.  We prove that the contraction number of the W-cycle
algorithm with a suffciently large number of smoothing steps is bounded away
from 1 uniformly.  We also show that the symmetric variable V-cycle algorithm
is an optimal preconditioner.