Path following methods for steady laminar Bingham flow in cylindrical pipes
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 43 (2009) no. 1 , p. 81-117
doi : 10.1051/m2an/2008039
URL stable : http://www.numdam.org/item?id=M2AN_2009__43_1_81_0

Classification:  47J20,  76A10,  65K10,  90C33,  90C46,  90C53
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 carried out.

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