Computational bases for RTkRTk and BDMkBDMk on triangles

In this article, we derive computational bases for Raviart–Thomas (RTRT) and Brezzi–Douglas–Marini (BDMBDM) (vector) approximation spaces on a triangulation of a domain in R2R2. The basis functions, defined on the reference triangle, have a Lagrangian property. The continuity of the normal component of the approximation across the edges in the triangulation is satisfied by the use of the Piola transformation and the Lagrangian property of the basis functions. A numerical example is given demonstrating the approximation property of the bases.