On the numerical solution of a boundary value problem in the plane elasticity for a double-connected domain Original Research Article

In this paper, we present an algorithm for numerical solution of some type of the inclusion problem in planar linear elastostatics. This problem arises on numerical solution of an inverse problem that contains in the identification of interfaces or inclusions by elastic boundary measurements. The algorithm is based on the boundary integral equation method. By combination of the single- and double-layer potentials a boundary value problem is reduced to a system of integral equations of the first kind with logarithmic and hypersingular kernels. Full discretization is realized by trigonometric quadrature method. We establish convergence of the method and prove error estimates in a Hölder space setting. Numerical examples illustrate convergence results.