The method of successive approximations for solving quasi-variational Signorini inequality

We consider the method of successive approximations for solving the semicoercive quasi-variational Signorini inequality corresponding to the contact problem of elasticity theory with friction. Each outer step of the iterative process involves the Signorini problem with given friction, which is solved by the Uzawa method based on an iterative proximal regularization of a modified Lagrangian functional. We investigate stabilization sequence of auxiliary finite element solutions on the outer steps of the method of successive approximations and present the results of numerical calculation.