On grid approximation accuracy of the elastisity theory problems with singularities of crack type

The integral representations of solutions of grid problems of elastisity theory for plane with cut, at the edges of which the conditions of the first or second kind are given, are found. It is shown that the accuracy is $O(h/r^{1/2})$ where r is a distance to cut apex. Modifications of difference schemes and schemes of finite element method raising the accuracy to $O(h^2)$ outside a finite neighbourhood of cut apex are constructed. The results of numerical calculations are attached.