Discrete qualocation methods for logarithmic-kernel integral equations on a piecewise smooth boundary

We consider a fully discrete qualocation method for Symm’s integral equation. The method is that of Sloan and Burn (1992), for which a complete analysis is available in the case of smooth curves. The convergence for smooth curves can be improved by a subtraction of singularity (Jeon and Kimn, 1996). In this paper we extend these results for smooth boundaries to polygonal boundaries. The analysis uses a mesh grading transformation method for Symm’s integral equation, as in Elschner and Graham (1995) and Elschner and Stephan (1996), to overcome the singular behavior of solutions at corners.