Numerical solution of boundary integral equations of the plane theory of elasticity in curvilinear polygons

A numerical method for solving boundary integral equations of the plane theory of elasticity in domains with piecewise analytic boundaries and a finite number of corner points is proposed. This method is based on the application of a family of composite quadrature formulas on condensing grids. It is proved that the proposed method is exponentially convergent with respect to the number of quadrature nodes in use.