A Decomposition of the Raviart-Thomas Finite Element into a Scalar and an Orientation-Preserving Part

Abstract

This contribution considers the conforming finite element discretizations the vector-valued function space H(div,Ω) in 2 and 3 dimensions. A new set of basis functions on simplices is introduced, using a decomposition into an orientation setting part with the edgewise constant normal flux as a degree of freedom and an orientation preserving higher-order part. As a simple combination of lowest-order Raviart-Thomas elements and higher order Lagrange-elements, the basis is suited for fast assembling strategies.

Full document