A comparison of hierarchical and interpolatory basis functions in the finite element analysis of waveguiding structures

The application of p- or hp-refinement techniques on an adaptive finite element procedure requires the use of hierarchical basis functions in order to facilitate the tangential continuity of the solution on the interface between two elements with different order. Interpolatory and hierarchical are nowadays well-established families of basis functions. Hierarchical basis functions have been used already in antenna analysis. In this paper, this kind of basis functions is employed in the full-wave analysis of closed waveguiding structures, which requires scalar/vector interpolation and is compared with interpolatory basis functions, mainly in terms of their convergence.