Tangential vector finite elements (TVFE's) overcome most of the shortc
omings 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 orde
r 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 thr
ee-dimensional equivalent of hierarchical mixed-order TVFE's for a tri
angular element, They can be formulated for higher orders than 2.5, an
d the generalization to curved tetrahedral elements is straightforward
.