This paper is devoted to the numerical solution of stationary
laminar Bingham fluids by path-following methods. By using duality theory, a
system that characterizes the solution of the original problem is derived.
Since this system is ill-posed, a family of regularized problems is obtained
and the convergence of the regularized solutions to the original one is proved.
For the update of the regularization parameter, a path-following method is
investigated. Based on the differentiability properties of the path, a model of
the value functional and a correspondent algorithm are constructed. For the
solution of the systems obtained in each path-following iteration a semismooth
Newton method is proposed. Numerical experiments are performed in order to
investigate the behavior and efficiency of the method, and a comparison with a
penalty-Newton-Uzawa-conjugate gradient method, proposed in [Dean et al., J. Non-Newtonian Fluid Mech.
142 (2007) 36–62], is