ERROR ANALYSIS OF A BOUNDARY ELEMENT COLLOCATION METHOD FOR A SCREEN PROBLEM IN R3

We examine the numerical approximation of the first-kind integral equation on a plane rectangle defined by the single-layer potential of the three-dimensional Laplacian. The solution is approximated by nodal collocation with piecewise bilinear trial functions on a rectangular grid. We prove stability and convergence of this method in the Sobolev space H-1/2 approximately. A key ingredient in the proof is the observation that the collocation equations define symmetric positive definite Toeplitz matrices.