Third-order Nedelec tetrahedral finite element

Abstract

The practical implementation of the third-order tetrahedral version of Nedelec's first family of curl-conforming elements is presented. Following the definition of the element given by Nedelec, the third-order vectorial basis functions of the element are deduced. The element thus obtained exhibits some important differences with respect to other higher-order curl-conforming elements which have appeared in the literature. Specifically, the third-order curl-conforming finite element proposed leads to better conditioned finite element method (FEM) matrices.