Cubature rule associated with a discrete blending sum of quadratic spline quasi-interpolants

A new cubature rule for a parallelepiped domain is defined by integrating a discrete blending sum of C1C1 quadratic spline quasi-interpolants in one and two variables. We give the weights and the nodes of this cubature rule and we study the associated error estimates for smooth functions. We compare our method with cubature rules based on the tensor products of spline quadratures and classical composite Simpson’s rules.