Estimating quadrature errors for an efficient method for quasi-singular boundary integral

The numerical resolution of the boundary integral equations applied to the differential equations of Laplace, Helmholtz and Maxwell requires the handling of quasi-singular integrals with different order of singularity. The numerical approximation of the integral equations of different kinds is made by boundary finite elements. In this paper, we present a complete survey for estimating quadrature errors for the numerical techniques proposed by Huang and Cruse [Q. Huang, T.A. Cruse, Some notes on singular integral techniques in boundary element analysis, Int. J. Numer. Methods Eng. 36 (15) (1993) 2643-2659], to calculate the quasi-singular integrals. To validate the accuracy and efficiency of these techniques and approve our study some numerical examples are presented and discussed.