We investigate the use of one-way cascadic multigrid strategies (CMG)
in the solution of incompressible viscous flow using the finite element
method. First we describe the basic CMG approach for representative elliptic
boundary value problems and summarize the theoretical error estimates from
approximation theory, desired smoother properties, and arithmetic complexity
of the method. The extension of these error and complexity estimates to
adaptive grids is also given. Then we present the mathematical formulation
and the finite element approximation scheme for the class of fluid-thermal
problems of interest. In supporting numerical experiments, we examine
performance of the algorithm on both serial and distributed parallel systems.
We carry out comparison studies with the standard BCG solution strategy on
the fine level grid and study diagonal treatments for zero pressure blocks.