ON QUADRATURE METHODS FOR THE DOUBLE-LAYER POTENTIAL EQUATION OVER THE BOUNDARY OF A POLYHEDRON

In this paper we consider a quadrature method for the solution of the double layer potential equation corresponding to Laplace's equation in a three-dimensional polyhedron. We prove the stability for our method in case of special triangulations over the boundary of the polyhedron. The assumptions imposed on the triangulations are analogous to those appearing in the one-dimensional case. Finally, we establish the rates of convergence and discuss the effect of mesh refinement near the corners and edges of the polyhedron.