Second-Order Nédélec Curl-Conforming Prismatic Element for Computational Electromagnetics

A systematic approach to obtaining mixed-order curl-conforming basis functions for a triangular prism is presented; focus is made on the second-order case. Space of functions for the prism is given. Basis functions are obtained as the dual basis with respect to suitably discretized Nédélec degrees of freedom functionals acting on elements of the space. Thus, the linear independence of the basis functions is assured while the belonging of the basis to the
a priori
given space of functions is guaranteed. Different strategies for the finite element assembly of the basis are discussed. Numerical results showing the verification procedure of the correctness of the implemented basis functions are given. Numerical results about sensibility of the condition number of the basis obtained concerning the quality of the elements of the mesh are also shown. Comparison with other representative sets of basis functions for prisms is included.