  This paper considers an enhancement of the classical iterated penalty Picard
(IPP) method for the incompressible Navier-Stokes equations, where we restrict
our attention to $O(1)$ penalty parameter, and Anderson acceleration (AA) is
used to significantly improve its convergence properties. After showing the
fixed point operator associated with the IPP iteration is Lipschitz continuous
and Lipschitz continuously (Frechet) differentiable, we apply a recently
developed general theory for AA to conclude that IPP enhanced with AA improves
its linear convergence rate by the gain factor associated with the underlying
AA optimization problem. Results for several challenging numerical tests are
given and show that IPP with penalty parameter 1 and enhanced with AA is a very
effective solver.
