Hierarchical High Order Finite Element Approximation Spaces for H(div) and H(curl)

Abstract

The aim of this paper is to present a systematic procedure for the construction of a hierarchy of high order finite element approximations for H(div) and H(curl) spaces based on quadrilateral and triangular elements with rectilinear edges. The principle is to chose appropriate vector fields, based on the geometry of each element, which are multiplied by an available set of H 1 hierarchical scalar basic functions. We show that the resulting local vector bases can be combined to obtain continuous normal or tangent components on the elements interfaces, properties that characterize piecewise polynomial functions in H(div) or H(curl), respectively.