Systematic method for finding a hierarchical vector finite element of any order using the Nedelec criteria and a Webb basis

In this paper, a systematic method for finding a hierarchical, tangentially continuous, vector finite element in H(curl) of,my order is given. The proposed method satisfies the criteria proposed by Nedelec (1980). To achieve this goal, the work by Webb (1999) is used extensively. In fact, Webb´s gradient basis is used in this work, but a modification of his rotational basis is required to satisfy the criteria shown in this paper. Finally, a numerical simulation is given to illustrate the validity of the proposed finite elements.