C1C1 Superconvergent quasi-interpolation based on polar forms

In this paper, we use C1C1 cubic B-splines to construct the Hermite interpolant of any polynomial in terms of their blossom. Consequently, a simple method is presented to get superconvergence phenomenon of cubic spline quasi-interpolants at the knots of a uniform partition. Thanks to this phenomenon, the cubic spline quasi-interpolant provides an interesting approximation very accurate at the superconvergence points. Numerical results are given to illustrate the theoretical ones.