On the Stability of Continuous-Discontinuous Galerkin Methods for Advection-Diffusion-Reaction Problems
Provides a theoretical stability guarantee for a hybrid finite element method, relevant for computational fluid dynamics and transport problems.
The authors prove stability of a coupled continuous-discontinuous Galerkin method for advection-diffusion-reaction problems under a specific flow condition, supported by numerical experiments.
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.