A dual method for solving the equilibrium problem of a body containing a thin defect

An equilibrium problem of a two-dimensional body with a thin defect whose properties are characterized by a fracture parameter is considered. The problem is discretized, and an approximation accuracy theorem is proved. To solve the problem, a dual method based on a modified Lagrange functional is used. In computational experiments, when solving the direct problem, a generalized Newton's method is used with a step satisfying Armijo's condition.