On the approximation by product rules of weakly singular double integrals over the square

Double integrals with algebraic and/or logarithmic singularities are of interest in the application of boundary element method, e.g. linear theory of the aerodynamics of slender bodies of revolution and in many other fields, for example computational electromagnetics. Therefore, the numerical evaluation of such type of integrals deserves attention. In this connection we propose here product interpolatory rules based on suitable Jacobi zeros, giving numerical tests to show the goodness of the proposed algorithm as well as from a point of view of convergence also for the simplicity of implementation.