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