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Solution of the Contact Elasticity Problem Based on an Iterative Proximal Regularization Method for the Modified Lagrangian Functional

The method of successive approximation is considered for solving the contact elasticity problem which corresponds to the quasivariational Signorini problem. Auxiliary problems with given frictions arising from each external step of this method are solved by the Uzawa method with iterative proximal regularization of the modified Lagrangian functional. Stabilization of the sequence of auxiliary finite-element solutions of external steps of successive approximation is investigated. Numerical results are considered.