Abstract
This paper presents a new approach for accurate numerical evaluation of the two-dimensional hypersingular integral identity for boundary potential gradients. The scale dependence of the accuracy of numerical results, observed in calculations based on the standard C0 element discretization, is eliminated by applying the optimum value of a dimensionless parameter (scaling factor) that can control the errors of the finite parts or the principal values evaluated for the discretized integral identity. Numerical results for sample potential problems with mixed boundary conditions are presented and compared with corresponding analytical solutions. It is shown that the optimum value of the scaling factor can be determined through the error estimation for one-dimensional finite-part integrals with a polynomial density function and its corresponding quadratic approximation.
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