  The Uzawa algorithm is an iterative method for the solution of saddle-point
problems, which arise in many applications, including fluid dynamics. Viewing
the Uzawa algorithm as a fixed- point iteration, we explore the use of Anderson
acceleration (also known as Anderson mixing) to improve the convergence. We
compare the performance of the preconditioned Uzawa algorithm with and without
acceleration on several steady Stokes and Oseen problems for incompressible
flows. For perspective, we include in our comparison several other iterative
methods that have appeared in the literature. The results indicate that the
accelerated preconditioned Uzawa algorithm converges significantly faster than
the algorithm without acceleration and is competitive with the other methods
considered.
