THE ANALYSIS OF MULTIGRID ALGORITHMS
         FOR NONCONFORMING AND MIXED METHODS
         FOR SECOND ORDER ELLIPTIC PROBLEMS

                 Zhangxin Chen

         Department of Mathematics and Institute
      for Scientific Computation, Texas A&M University
         College Station, TX 77843--3404


                  Do Y. Kwak

       Department of Mathematics, Korea Advanced Institute
          cience and Technology, Taejon, Korea 305--701

Abstract.  In this paper we consider multigrid algorithms for nonconforming
and mixed finite element methods for second order elliptic problems on
triangular and rectangular finite elements.  We prove optimal convergence
properties of the W-cycle multigrid algorithm and uniform condition number
estimates for the variable V-cycle preconditioner.  Lower order terms are
treated, so our results also apply to parabolic equations.