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

Abstract

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.

Keywords:

• Boundary integral equations
• spline collocation
• hypersingular integral equation

AMS:

• 65N35
• 65N38