RECENT DEVELOPMENT OF MULTIGRID ALGORITHMS FOR
                       MIXED AND NONCONFORMING METHODS
                      FOR SECOND ORDER ELLIPTIC PROBLEMS

                      Zhangxin Chen and Richard E. Ewing


Due to its saddle point property, it is known that the linear systems arising
from the mixed method are generally harder to solve than those arising from
comparable Galerkin methods.  In particular, there has been little theory for
constructing good preconditioners and developing efficient multigrid methods
for solving the system of algebraic equations arising from the mixed method.
An alternate approach was suggested by means of a nonmixed formulation.
Namely, it is shown that the mixed finite element method is equivalent to a
modification of the nonconforming Galerkin method.  The author will talk about
recent development of multilevel preconditioners and multigrid methods for
solving the mixed method system.  Based on the nonmixed formulation for the
mixed method, we shall show that optimal order V and W-cycle multigrid
algorithms and algebraic multilevel preconditioners can be developed for the
system of algebraic equations.

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Institute for Scientific Computation 
and Department of Mathematics,
Texas A&M University, 
326 Teague Research Center, 
College Station, TX 77843--3404
Phone number: (409)847--9086
Fax: (409)845--6077 
Email: zchen@isc.tamu.edu
       ewing@ewing.tamu.edu