A novel class of hierarchical higher order tangential vector finite elements for electromagnetics

Node based finite elements are not suitable for modeling the vector nature of electromagnetic fields. Tangential vector finite elements (TVFEs) overcome most of the shortcomings of node based finite elements and for various element shapes, several TVFEs of different orders have previously been presented. For a triangular element, this paper presents a novel class of hierarchical higher order TVFEs that differs significantly from traditional TVFEs. For a simple application, the paper demonstrates that the performance of one of these new TVFEs is equivalent to the performance of a traditional mixed order TVFE. However, the hierarchical nature of the new TVFEs may make them a better choice than traditional TVFEs. A homogeneously filled rectangular waveguide is considered as an example.