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.
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