FIAT: enabling classical and modern macroelements

Many classical and modern finite element spaces are derived by dividing each computational cell into finer pieces. Such macroelements frequently enable the enforcement of mathematically desirable properties such as divergence-free conditions or \(C^{1}\) continuity in a simpler or more efficient manner than elements without the subdivision. Although a few modern software projects provide one-off support for particular macroelements, a general approach facilitating broad-based support has, until now, been lacking. In this work, we describe a major addition to the FIAT project to support a wide range of different macroelements. These enhancements have been integrated into the Firedrake code stack. We provide numerical evaluation of the new macroelement facility.