Isoparametric second order Ne´de´lec tetrahedral finite element

A rigorous implementation of the isoparametric second order Ne´de´lec tetrahedral element is presented. The basis functions are defined in the master element. A second-order Lagrange mapping is defined between each real element of the mesh and the master element. A classical projection approach and one based on the octree method may be used to obtain the mapping parameters. The basis functions of the real element are obtained by transforming as gradients the basis functions of the master element. Several numerical results of the application of the isoparametric element thus obtained in the context of the eigenvalue finite element analysis of microwave cavities are shown.