An analysis of quadrature errors in second-kind boundary integral methods

This paper considers the effect of quadrature errors on Galerkin methods for approximating the solution of second-kind Fredholm integral equations with weakly singular kernels defined on a smooth, closed surface in three dimensions. A quadrature strategy for Galerkin methods that use piecewise poly-nomials, both continuous and discontinuous, on a quadrilateral-based mesh is proposed. The error resulting from this further discretization is proved to be no larger than the original discretization error, and moreover, the amount of work needed to compute the resulting matrix for the corresponding linear system is shown to be proportional to the number of matrix entries.