Error estimates in the numerical evaluation of some BEM singular integrals

In some applications of Galerkin boundary element methods one has to comput e integrals which, after proper normalization, are of the form integral (b)(a)integral (1)(-1) f(x,y)/x-y dxdy, where (a, b) = (-1, 1), or (a, b) = (a, -1), or (a, b) = (1, b), and f(x, y ) is a smooth function. In this paper we derive error estimates for a numerical approach recently p roposed to evaluate the above integral when a p-, or h - p, formulation of a Galerkin method is used. This approach suggests approximating the inner i ntegral by a quadrature formula of interpolatory type that exactly integrat es the Cauchy kernel, and the outer integral by a rule which takes into acc ount the log endpoint singularities of its integrand. Some numerical exampl es are also given.