Higher order interpolatory vector bases on prism elements

Abstract

Triangular prism elements are useful in numerical solutions of electromagnetic field problems since they permit a three-dimensional (3-D) geometry to be generated by the extrusion of a triangular mesh. Few applications have employed vector basis functions on prism elements and the extension to distorted prisms reported in the literature apparently does not ensure cell-to-cell continuity. In this paper, we define interpolatory higher order curl- and divergence-conforming vector basis functions of the Nedelec type on prism elements, with extension to curved prisms, and discuss their completeness properties. Vector bases of arbitrary polynomial order are given and various results to confirm the faster convergence of higher order functions are presented.