High-order optimal edge elements for pyramids, prisms and hexahedra

Edge elements are a popular method to solve Maxwell’s equations especially in time-harmonic domain. However, when non-affine elements are considered, elements of the Nédélec’s first family [19] are not providing an optimal rate of the convergence of the numerical solution toward the solution of the exact problem in H(curl)-norm. We propose new finite element spaces for pyramids, prisms, and hexahedra in order to recover the optimal convergence. In the particular case of pyramids, a comparison with other existing elements found in the literature is performed. Numerical results show the good behavior of these new finite elements.