Error estimation of quadrature rules for evaluating singular integrals in boundary element problems

The e cient numerical evaluation of integrals arising in the boundary element method is of considerable practical importance. The superiority of the use of sigmoidal and semi-sigmoidal transformations together with Gauss{Legendre quadrature in this context has already been well-demonstrated numerically by one of the authors. In this paper, the authors obtain asymptotic estimates of the truncation errors for these algorithms. These estimates allow an informed choice of both the transformation and the quadrature error in the evaluation of boundary element integrals with algebraic or algebraic=logarithmic singularities at an end-point of the interval of integration