In the numerical solution of three dimensional (3-D) electromagnetic field
problems, the regions of interest can be discretized by elements having tet
rahedral, brick or prismatic shape. However, such different shape elements
cannot be linked to form a conformal mesh; to this purpose pyramidal elemen
ts are required, In this paper, we define interpolatory higher order curl-
and divergence-conforming vector basis functions on pyramidal elements, wit
h extension to curved pyramids, and discuss their completeness properties.
A general procedure to obtain vector bases of arbitrary polynomial order is
given and bases up to second order are explicitly reported. These new elem
ents ensure the continuity of the proper vector components across adjacent
elements of equal order but different shape. Results to confirm the faster
convergence of higher order functions on pyramids are presented.