High-order finite elements on pyramids. II: unisolvency and exactness
This provides a missing piece for high-order finite element methods on hybrid meshes, enabling more flexible and accurate simulations in computational science.
The paper completes the definition of high-order conforming finite elements on pyramids for de Rham complex spaces, proving unisolvency, compatibility with tetrahedral and hexahedral elements, and a commuting diagram property.
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.