Implementation of the continuous-discontinuous Galerkin finite element method

For the stationary advection-diffusion problem the standard continuous Galerkin method is unstable without some additional control on the mesh or method. The interior penalty discontinuous Galerkin method is more stable but at the expense of an increased number of degrees of freedom. The hybrid method proposed in [5] combines the computational complexity of the continuous method with the stability of the discontinuous method without a significant increase in degrees of freedom. We discuss the implementation of this method using the finite element library deal.ii and present some numerical experiments.