Hierarchical tangential vector finite elements for tetrahedra

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