On the Stability of Continuous-Discontinuous Galerkin Methods for   Advection-Diffusion-Reaction Problems
  We consider a finite element method which couples the continuous Galerkin method away from internal and boundary layers with a discontinuous Galerkin method in the vicinity of layers. We prove that this consistent method is stable in the streamline diffusion norm if the convection field flows non-characteristically from the region of the continuous Galerkin to the region of the discontinuous Galerkin method. The stability properties of the coupled method are illustrated by numerical experiments. 
Andrea Cangiani, John Chapman, Emmanuil Georgoulis, Max Jensen
math.NA