A Bernstein–Bézier Basis for Arbitrary Order Raviart–Thomas Finite Elements

A Bernstein–Bézier basis is developed for $${\varvec{H}}({{\mathrm{div}}})$$H(div)-conforming finite elements that gives a clear separation between the curls of the Bernstein basis for the polynomial discretization of the space $$H^1$$H1, and the noncurls that characterize the specific $${\varvec{H}}({{\mathrm{div}}})$$H(div) finite element space (Raviart–Thomas in our case). The resulting basis has two distinct components reflecting this separation with the basis functions in each component having a natural identification with a domain point, or node, on the element. It is shown that the basis retains the favorable properties of the Bernstein basis that were used in Ainsworth et al. (SIAM J Sci Comput 3087–3109, 2011) to develop efficient computational procedures for the application of the elements.