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In this paper, we propose a dual-mixed formulation for stationaryviscoplastic flows with yield, such as the Bingham or the Herschel-Bulkleyflow. The approach is based on a Huber regularization of the viscosity term anda two-fold saddle point nonlinear operator equation for the resulting weakformulation. We provide the uniqueness of solutions for the continuousformulation and propose a discrete scheme based on Arnold-Falk-Winther finiteelements. The discretization scheme yields a system of slantly differentiablenonlinear equations, for which a semismooth Newton algorithm is proposed andimplemented. Local superlinear convergence of the method is also proved.Finally, we perform several numerical experiments in two and three dimensionsto investigate the behavior and efficiency of the method.

A Dual-Mixed Approximation for a Huber Regularization of Generalized $p$-Stokes Viscoplastic Flow Problems