Mixed Discontinuous Galerkin methods for Darcy flow

We consider a family of mixed finite element discretizations of the Darcy low equations using totally discontinuous elements (both for the pressure and the flux variable). Instead of using a jump stabilization as it is usually done for DG methods we use the residual-based stabilization iof Hughes-Franca type. We show that such stabilization works for discontinuous elements as well, provided both the pressure and the flux are approximated by local polynomials of degree greater than or equal to 1, without any need for additional jump terms.