Application of the quadrature method for solving boundary integral equations of plane elasticity theory on polygons

A method for the numerical solution of a class of boundary integral equations in the plane theory of elasticity on curves forming the boundary of simply connected polygons is proposed. Under some restrictions on geometry of domains, we prove the existence and uniqueness of solutions to approximating systems of linear algebraic equations. Several estimates of stability are obtained. The exponential rate of convergence for this method is proved in C-norm. The work was supported by the Russian Foundation for Basic Research (99–01–01146) and by the Scientific Program “Universities of Russia” (UR.04.03.002).