AN OPTIMAL ORDER NONNESTED MIXED MULTIGRID
METHOD FOR GENERALIZED STOKES PROBLEMS
Qingping Deng
Department of Mathematics
The University of Tennessee
Knoxville, TN 37996
deng@math.utk.edu
Abstract. A multigrid algorithm is developed and analyzed for generalized
Stokes problems discretized by various nonnested mixed finite elements within
a unified framework. It is abstractly proved by an element-independent
analysis that the multigrid algorithm converges with an optomal order if there
exists a "good" prolongation operator. A trick to construct a "good"
prolongation operator for nonnested multilevel finite element spaces is
proposed. Its basic idea is to introduce a sequence of auxiliary nested
multilevel finite element spaces and define a prolongation operator as a
composite operator of two single grid level operators. This makes not only
the construction of a prolongation operator is much easy (but the final
explicity forms of such prolongation operators are fairly simple), but also
the verification of the approximate propertis for prolongation operators is
much simplified. Finally, as an application, the framewoek and trick is
applied to eight typical nonnested mixed finite elements.