On a stable duality scheme method for solution of the Mosolov and the Miasnikov problem with boundary friction

The paper deals with the construction of a stable method for solution of the Mosolov and the Miasnikov variational problem with boundary friction and can be considered as the sequel of the investigations started in [1]. An approximate solution is carried out on the basis of the iterative prox-regularization method. In this case, each auxiliary problem is coming to the search of the Lagrange functional saddle point. The error estimation is defined for the numerical solution of the problem in the case of realization of this algorithm using the finite element method on a sequence of triangulations. The results of numerical computations are presented.