COARSE-GRID CORRECTION OF VERY SMOOTH ERROR-COMPONENTS

                                 Irad Yavneh

Coarse-grid correction operators are evaluated in the context of their ability
to correct asymptotically smooth error components.  The requirements for
elliptic and nonelliptic problems are compared for both Galerkin coarsening
and coarsening schemes based on the differential operator.  For Galerkin
coarsening minimal requirements for the orders of the intergrid transfers used
in defining the coarse-grid operator are given, and questions are raised
regarding the usability of the so-called "approximation property" as a
practical criterion.  Various well-known coarsening schemes are compared in
the present context for first-order accurate advection operators and a winner
is declared.