Discontinuous Galerkin finite element methods with shock-capturing for nonlinear convection dominated models

• We solve convection dominated diffusion problems with nonlinear reaction terms.
• We use the upwind symmetric interior penalty Galerkin (SIPG) discretization.
• Unphysical oscillations occur due to the layers and the nonlinear reaction terms.
• A shock-capturing with discontinuity detection is used to eliminate oscillations.

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 where unphysical oscillations occur. Finally, the proposed method is tested on various single- and multi-component problems.