Two condensed macro-elements with full approximation power (Q963253)

The Powell-Sabin macro-element is a classical tool for piecewise polynomial approximations in two dimensions. This is enhanced in this paper by considering macro elements which have fewer degrees of freedom and require only data at the vertices. The new element is defined and the dimension of the appropriate spline space is computed. Uniqueness and stability are considered, too. Further, an extension of the element to three dimensions is made, where again the dimension is computed and stability and uniqueness are shown.