  We consider two modifications of the Arrow-Hurwicz (AH) iteration for solving
the incompressible steady Navier-Stokes equations for the purpose of
accelerating the algorithm: grad-div stabilization, and Anderson acceleration.
AH is a classical iteration for general saddle point linear systems and it was
later extended to Navier-Stokes iterations in the 1970's which has recently
come under study again. We apply recently developed ideas for grad-div
stabilization and divergence-free finite element methods along with Anderson
acceleration of fixed point iterations to AH in order to improve its
convergence. Analytical and numerical results show that each of these methods
improves AH convergence, but the combination of them yields an efficient and
effective method that is competitive with more commonly used solvers.
