Macro-elements of arbitrary smoothness over the Clough-Tocher split of a triangle

Abstract

In this chapter, the bivariate Cr macro-elements over the Clough-Tocher split of a triangle from Matt [66] are considered. They are more general than the bivariate Cr macro-elements based on the Clough-Tocher split constructed in [59], since they can be extended to splines of higher degree. Thus, the bivariate macro-elements considered here form a basis for the construction of the trivariate macro-elements of arbitrary smoothness over theWorsey-Farin split of a tetrahedron (see chapter 8).