Hierarchical vector polynomials for the triangular prism

Abstract

A new set of hierarchical vector basis functions that spans the curl-conforming reduced-gradient spaces of Nédélec on a triangular-prism cell is presented. These functions are constructed from orthogonal scalar polynomials to enhance their linear independence, which is a simpler process than an orthogonalization applied to the final vector functions. The new functions are compatible with those recently developed for tetrahedral and brick cells, in the sense that vector functions on a triangular face of a tetrahedron (or on a quadrilateral face of a brick) can easily be made continuous with analogous functions on the triangular (or quadrilateral) face of a prism cell. Specific functions are tabulated to order 3.5.