The computation of potentials near and on the boundary by an extraction technique for boundary element methods

Here, we present the two-dimensional version of a bootstrapping algorithm for the computation of arbitrary derivatives of the Cauchy data and for the extraction of potentials near and on the boundary for the Laplacian if corresponding boundary integral equations are used. The method employs the derivatives of the Green representation formula in terms of Cauchy singular or weakly singular integrals and also their compositions with derivatives. It allows the robust and superconvergent numerical evaluation of potentials and their derivatives up to and on the boundary curve. Furthermore, we determine a criterion whether to use the traditional Green representation formula or our extraction technique for the point evaluation of the potentials in the domain.

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