Superconvergent local quasi-interpolants based on special multivariate quadratic spline space over a refined quadrangulation

In this paper, we first recall some results concerning the construction and the properties of quadratic B-splines over a refinement Δ of a quadrangulation ◊ of a planar domain introduced recently by Lamnii et al. Then we introduce the B-spline representation of Hermite interpolant, in the special space S21,0(Δ), of any polynomial or any piecewise polynomial over refined quadrangulation Δ of ◊. After that, we use this B-representation for constructing several superconvergent discrete quasi-interpolants. The new results that we present in this paper are an improvement and a generalization of those developed in the above cited paper.