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In this paper we present a new class of cubature rules with the aim ofaccurately integrating weakly singular double integrals. In particular we focuson those integrals coming from the discretization of Boundary IntegralEquations for 3D Laplace boundary value problems, using a collocation methodwithin the Isogeometric Analysis paradigm. In such setting the regular part ofthe integrand can be defined as the product of a tensor product B-spline and ageneral function. The rules are derived by using first the splinequasi-interpolation approach to approximate such function and then theextension of a well known algorithm for spline product to the bivariatesetting. In this way efficiency is ensured, since the locality of any splinequasi-interpolation scheme is combined with the capability of an ad--hoctreatment of the B-spline factor. The numerical integration is performed on thewhole support of the B-spline factor by exploiting inter-element continuity ofthe integrands

Cubature rules based on bivariate spline quasi-interpolation for weakly singular integrals