190 research outputs found
Semismooth Newton and Augmented Lagrangian Methods for a Simplified Friction Problem
International audienceIn this paper a simplified friction problem and iterative second-order algorithms for its solution are analyzed in infinite dimensional function spaces. Motivated from the dual formulation, a primal-dual active set strategy and a semismooth Newton method for a regularized problem as well as an augmented Lagrangian method for the original problem are presented and their close relation is analyzed. Local as well as global convergence results are given. By means of numerical tests, we discuss among others convergence properties, the dependence on the mesh, and the role of the regularization and illustrate the efficiency of the proposed methodologies. 1. Introduction. This paper is devoted to the convergence analysis of iterative algorithms for the solution of mechanical problems involving friction. As a model problem we consider a simplified friction problem that can be stated as the minimization of the nondifferentiable functional J(y) :
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