A hybridizable discontinuous Galerkin method for steady-state convection-diffusion-reaction problems

We consider a novel discontinuous Galerkin method for convection-diffusion-reaction problems, characterized by three main properties. The first is that the method is hybridizable; this renders it efficiently implementable. The second is that, when the method uses polynomial approximations of the same degree for both the total flux and the scalar variable, optimal convergence properties are obtained for both variables. The third is that it is possible to postprocess in an element-by-element fashion the solution to obtain an approximation of the scalar variable which converges faster than the original one.

The proposed method is compared with other well established methods concerning the accuracy of the results and the computational cost, both in the diffusion dominated regime and in the convection dominated regime. Our analysis indicates that the hybridizable discontinuous Galerkin formulation is a viable alternative to the more classical approaches; in particular, it shows that the typical benefits of the mixed finite element methods can be obtained at a computational cost comparable to that of the standard primal continuous formulation.