On the assembly of 3D higher-order Nedelec curl-conforming tetrahedral elements

In previous publications, the authors have proposed a methodology for the practical implementation of the Nedelec's (1980) first family of curl-conforming tetrahedral elements. The implementations corresponding to orders higher than one exhibit important differences with respect to those appeared in the literature. This paper deals with the assembly of the higher-order finite elements thus obtained. In particular, two different options are proposed to define the degrees of freedom associated to the faces of neighboring elements. Both options allow one to perform the computations over the parent element, while providing the tangential continuity through elements when utilizing the conventional finite element assembly procedure. The advantages and disadvantages of the two options are compared.