Hierarchical tangential vector finite elements for tetrahedra

Tangential vector finite elements (TVFEs) overcome most of the shortcomings of node-based finite elements for electromagnetic simulations. Hierarchical TVFEs are of considerable practical interest since they allow use of effective selective field expansions where different order TVFEs are combined within a computational domain. For a tetrahedral element, this letter proposes a set of hierarchical mixed-order TVFEs up to and including order 2.5 that differ from previously presented TVFEs. The hierarchical mixed-order TVFEs are constructed as the three-dimensional equivalent of hierarchical mixed-order TVFEs for a triangular element. They can be formulated for higher orders than 2.5, and the generalization to curved tetrahedral elements is straightforward.