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 t...

In this paper, convection-diffusion-reaction models with nonlinear reaction mechanisms, which are typical problems of chemical systems, are studied by using the upwind symmetric interior penalty Galerkin (SIPG) method. The local spurious oscillations are minimized by adding an artificial viscosity diffusion term to the original equations. A discontinuity sensor is used to detect the layers wher...