A hybrid discontinuous Galerkin method for advection–diffusion–reaction problems

A hybrid discontinuous Galerkin (HDG) method for the Poisson problem introduced by Jeon and Park can be viewed as a hybridizable discontinuous Galerkin method using a Baumann–Oden type local solver. In this work, an upwind HDG method with super-penalty is proposed to solve advection–diffusion–reaction problems. A super-penalty formulation facilitates an optimal order convergence in the L2L2 norm as well as the energy norm. Several numerical examples are presented to show the performance of the method.