  This paper studies a finite element discretization of the regularized Bingham
equations that describe viscoplastic flow. An efficient nonlinear solver for
the discrete model is then proposed and analyzed. The solver is based on
Anderson acceleration (AA) applied to a Picard iteration, and we show
accelerated convergence of the method by applying AA theory (recently developed
by the authors) to the iteration, after showing sufficient smoothness
properties of the associated fixed point operator. Numerical tests of spatial
convergence are provided, as are results of the model for 2D and 3D driven
cavity simulations. For each numerical test, the proposed nonlinear solver is
also tested and shown to be very effective and robust with respect to the
regularization parameter as it goes to zero.
