Construction of Hierarchic Families of Finite Elements by Localization of Their Degrees of Freedom

Hierarchic families of finite elements are widely used in higher order finite-element methods. Several hierarchic sets of basis functions for nodal, edge, and face elements are proposed by different authors in scientific literature. However, no general methodology exists for their construction. This paper presents an analysis of hierarchic families of finite elements which leads to the localization of their degrees of freedom. From this localization, we derive an algebraic approach for the construction of hierarchic families of nodal, edge, and face elements. The case of tetrahedral finite elements is discussed in detail.