  We consider the elastic stress near a hole with corners in an infinite plate
under biaxial stress. The elasticity problem is formulated using complex
Goursat functions, resulting in a set of singular integro-differential
equations on the boundary. The resulting boundary integral equations are solved
numerically using a Chebyshev collocation method which is augmented by a
fractional power term, derived by asymptotic analysis of the corner region, to
resolve stress singularities at corners of the hole. We apply our numerical
method to the test case of the hole formed by two partially-overlapping
circles, which can include either a corner pointing into the solid or a corner
pointing out of the solid. Our numerical results recover the exact stress on
the boundary to within relative error $10^{-3}$ for modest computational
effort.
