A Numerical Boundary Eigenvalue Problem for Elastic Cracks in Free and Half Space

Abstract

We present in this paper a numerical method for hypersingular boundary integral equations. This method was developed for planar crack problems: additional edge singularities are known to develop in that case. This paper includes a rigorous error analysis proving the convergence of our numerical scheme. Three types of examples are covered: the Laplace equation in free space, the linear elasticity equation in free space, and in half space.