  We propose, analyze and test Anderson-accelerated Picard iterations for
solving the incompressible Navier-Stokes equations (NSE). Anderson acceleration
has recently gained interest as a strategy to accelerate linear and nonlinear
iterations, based on including an optimization step in each iteration. We
extend the Anderson-acceleration theory to the steady NSE setting and prove
that the acceleration improves the convergence rate of the Picard iteration
based on the success of the underlying optimization problem. The convergence is
demonstrated in several numerical tests, with particularly marked improvement
in the higher Reynolds number regime. Our tests show it can be an enabling
technology in the sense that it can provide convergence when both usual Picard
and Newton iterations fail.
