High-order finite elements on pyramids. II: unisolvency and exactness

Abstract: We present degrees of freedom to accompany the approximation spaces already presented in a companion paper and thus complete the definition of families of high-order conforming finite elements on pyramids for the spaces of the de Rham complex. We prove that the elements are unisolvent; are compatible with conventional tetrahedral and hexahedral elements; satisfy a commuting diagram property and contain high-degree polynomials. We also tabulate shape functions for each element.