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Hybridized Discontinuous Galerkin Method for Convection-Diffusion-Reaction Problems

In this paper, we propose a new hybridized discontinuous Galerkin method for the convection-diffusion-reaction problems with mixed boundary conditions. The coercivity of the convection-reaction part is achieved by adding an upwinding term. We give error estimates of optimal order in the piecewise H1-seminorm. Furthermore, we show that the approximate solution of our scheme is close to that of the reduced problem when the diffusion coefficient is very small. Some numerical results are presented to verify the validity of our method.