Stable algorithm for solving the semicoercive problem of contact of two bodies with friction on the boundary

The problem of one-sided contact of two elastic bodies is considered. This is a static displacement problem. The bodies are influenced by bulk and surface forces, in the contact area there are friction forces. The substantiation of using the method of modified Lagrange functionals is given. The method of successive displacement is applied to the solution of a finite-dimensional analog of a task. To solve a finite-dimensional problem, the pointwise relaxation method is used. The results of numerical calculations are given.