M. Ainsworth and G. Andriamaro and O. Davydov, A Bernstein-Bézier basis for arbitrary order Raviart-Thomas finite elements, Constr. Approx., 41 (2015), 1-22. doi:10.1007/s00365-014-9269-8

Abstract: A Bernstein-Bézier basis is developed for $\b{H}(\Div)$-conforming finite elements that gives a clear separation between the \emph{curls} of the Bernstein basis for the polynomial discretisation of the space $H^1$, and the non-curls that characterize the specific $\b{H}(\Div)$ 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 favourable properties of the Bernstein basis that were used in [1] to develop efficient computational procedures for the application of the elements.

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