The collocation method for first-kind boundary integral equations on polygonal regions

Abstract

In this paper the collocation method for first-kind boundary integral equations, by using piecewise constant trial functions with uniform mesh, is shown to be equivalent to a projection method for second-kind Fredholm equations. In a certain sense this projection is an interpolation projection. By introducing this technique of analysis, we particularly consider the case of polygonal boundaries. We give asymptotic error estimates in L 2 {L_2} norm on the boundaries, and some superconvergence results for the single layer potential.