Constructing differential quasi-interpolants on uniform partitions. An approach based on the Bernstein-Bezier representation

We propose a general construction of differential quasi-interpolants based on a B-spline defined on a uniform partition. After obtaining an appropriate expression of the quasiinterpolation error and using the Bernstein-Bezier representation of the B-spline, we define and solve a minimization problem. The solutions of that problem provide the differential quasi-interpolation operators. A bivariate example will be presented.