Explicit construction of computational bases for RTk and BDMk spaces in R3

In this paper, a set of computational bases is developed for Raviart-Thomas (RT) and Brezzi-Douglas-Marini (BDM) vector spaces in R3. There are two attractive computational features of the bases. The first is that the normal components of the basis functions satisfy a Lagrangian property with respect to the nodal points in the faces of the tetrahedrons in the triangulation. The second computationally attractive feature is a decomposition of the basis function into face functions and interior functions, permitting a significant reduction in the number of unknown coefficients in the approximating linear system arising in a finite element computation.