Third-order Nedelec curl-conforming finite element

The third-order version of Nedelec's first family of curl-conforming elements over simplices is presented. Following the definition of the element given by Nedelec, the third-order vector basis functions are deduced. The elements thus obtained exhibit some important differences with respect to other higher-order curl-conforming elements appeared in the literature. Among other features, the proposed third-order curl-conforming finite element leads to better conditioned finite-element method matrices.