Mesh grading for integral equations of the first kind with logarithmic kernel

When the Galerkin method is used to solve the first kind integral equations with logarithmic kernel on polygons or open arcs, the singularities of the solution degrade the rates of convergence. The aim of this paper is to show, for the particular case of piecewise-constant approximation spaces, that in some cases the $O(h^3 )$ order of convergence can be restored by a suitable grading of the mesh.