A COMBINED HYBRIDIZED DISCONTINUOUS GALERKIN/HYBRID MIXED METHOD FOR VISCOUS CONSERVATION LAWS

Recently, we have proposed a method for solving steady-state convection-diffusion equations, including the full compressible Navier-Stokes equations [19]. The method is a combination of a mixed Finite Element method for the diffusion terms, and a Discontinuous Galerkin method for the convection term. The method is fully implicit, and the globally coupled unknowns are the hybrid variables, i.e., variables having support on the skeleton of the mesh only. This reduces the amount of overall degrees of freedom tremendously. In this paper, we extend our method to be able to cope with time-dependent convection-diffusion equations, where we use a dual time-stepping method in combination with backward difference schemes.