Convergence of boundary element collocation methods for dirichlet and neumann screen problems in R3

摘要

We study the numerical approximation of two pseudodifferential equations on a plane rectangle defined by the single layer potential and by the normal derivative of the double layer potential of the three-dimensional Laplacian. The solutions are approximated by nodal collocation with piecewise bilinear, respectively by bicubic, trial functions on a rectangular grid. The result for the single layer potential was already derived in 7. We present an alternative proof for the single layer potential and derive for the first time the convergence result for a collocation method for the hypersingular integral equation on the rectangle.