The Hybridizable Discontinuous Galerkin Method

Abstract

In this section, we show how the spaces of RT and BDM can be balanced to have an equal polynomial degree. Stability will be restored using a discrete stabilization (not penalization) function. This is how local quantities of RT, BDM, and HDG methods compare. Note that there is no natural finite element structure for ${\mathbf {q}}_h$, where we can recognize boundary and internal degrees of freedom. Instead, we will have a projection that integrates $({\mathbf {q}}_h, u_h)$ into the same structure.