A numerical investigation of convection-dominated convection diffusion problems using characteristic stabilized mixed finite element method

In this paper, we propose a characteristic stabilized mixed finite element method based on the lower regularity of the flux for convection dominated convection diffusion problems. The method combines the characteristic method with a stabilized mixed finite element method that uses the lowest equal-order pair for the velocity and pressure. The stabilization term is based on two local Gauss integrations for the velocity. Moreover, we obtain that the approximation of the pressure $u$ is optimal in the $L^2$-norm and $H^1$-norm, the approximation of the velocity $p$ is suboptimal in the $L^2$-norm. Finally, numerical experiments in 2D and 3D are presented to verify the theoretical results.