On the inexact symmetrized globally convergent semi-smooth Newton method for 3D contact problems with Tresca friction: the R-linear convergence rate

Abstract

The semi-smooth Newton method for solving discretized contact problems with Tresca friction in three-dimensional space is analysed. The slanting function is approximated to get symmetric inner linear systems. The primal-dual algorithm is transformed into the dual one so that the conjugate gradient method can be used. The R-linear convergence rate is proved for an inexact globally convergent variant of the method. Numerical experiments conclude the paper.