Higher order interpolatory vector bases on pyramidal elements

In the numerical solution of three-dimensional (3-D) electromagnetic field problems, the regions of interest can be discretized by elements having tetrahedral, brick or prismatic shape. However, such different shape elements cannot be linked to form a conformal mesh; to this purpose pyramidal elements are required. In this paper, we define interpolatory higher order curl- and divergence-conforming vector basis functions on pyramidal elements, with 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 elements 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