Systematic construction of three-dimensional ultra high-order Nedelec's elements

A new systematic construction of the three-dimensional ultra high-order Nedelec's elements is presented in this paper. It is proposed that a set of vector basis functions be simply chosen out of irrotational and rotational vector polynomials. Vector shape functions of the element are uniquely derived by the conditions modified from the scalar elements. The significance of the positions and directions of the arrows in the Nedelec's element is described. The higher order elements are also implemented in a cavity analysis.