  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.
