Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)This paper considers a systematic procedure for the construction of a hierarchy of high order finite element approximation for Hdiv and Hcurl spaces based on triangular and quadrilateral partitions of bidimensional domains. The principle is to choose an appropriate set of vectors, based on the geometry of each element, which are multiplied by an available set of H-1 hierarchical scalar basic functions. This strategy produces vector basis functions with continuous normal or tangent components on the elements interfaces, properties that characterise functions in Hdiv or Hcurl, respectively. We also present a numerical study to evaluate the correct balancedness of the resulting Hdiv spaces of degree k and L-2 spaces of degree k - 1 on the resolution of the mixed formulation for a Steklov eigenvalue problem. (c) 2012 Elsevier B.V. All rights reserved.240SI204214Brazilian National Agency of Petroleum, Natural Gas and Biofuels (ANP - PETROBRAS)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)