ITERATIVE SOLUTION OF LINEAR-SYSTEMS ARISING FROM THE NYSTROM METHOD FOR THE DOUBLE-LAYER POTENTIAL EQUATION OVER CURVES WITH CORNERS

In this paper we consider a quadrature method for the solution of the double-layer potential equation corresponding to Laplace's equation in a polygonal domain. We prove the stability for our method in case of special triangulations over the boundary or the polygon. For the solution of the corresponding system of linear equations, we consider a two-grid iteration and establish the rates of convergence and complexity. Finally, we discuss the effect of mesh refinement near the corners of the polygon.