  In this paper, we propose a dual-mixed formulation for stationary
viscoplastic flows with yield, such as the Bingham or the Herschel-Bulkley
flow. The approach is based on a Huber regularization of the viscosity term and
a two-fold saddle point nonlinear operator equation for the resulting weak
formulation. We provide the uniqueness of solutions for the continuous
formulation and propose a discrete scheme based on Arnold-Falk-Winther finite
elements. The discretization scheme yields a system of slantly differentiable
nonlinear equations, for which a semismooth Newton algorithm is proposed and
implemented. Local superlinear convergence of the method is also proved.
Finally, we perform several numerical experiments in two and three dimensions
to investigate the behavior and efficiency of the method.
