Multi-sided macro-element spaces based on Clough-Tocher triangle splits with applications to hole filling

Cr macro-element spaces are constructed on polygonal domains with an arbitrary number of sides. The spaces consist of polynomial supersplines defined on triangulations which have been partially refined with Clough-Tocher splits. In addition to giving dimension formulae, minimal determining sets, and nodal bases, we derive error bounds for the corresponding Hermite interpolation operators. A number of examples are presented to show how the spaces can be used to fill n-sided holes.