Streamline diffusion weak Galerkin finite element methods for linear unsteady state convection diffusion equations and error analysis (Q6618044)

The authors are concerned with the numerical solution to an initial-boundary value problem for the linear 2D unsteady (not unstable! See the introduction) convection-diffusion equation. The authors assume a moderate dominant convective regime. They design a Galerkin streamlined diffusion method that introduces a diffusion term only in the direction of the streamlines. In a rather naive manner, they analyse the stability of the process and carry out some numerical experiments. Anyway, the numerical results presented do not show anything spectacular like the sharp gradient of the solution (boundary layer) in the case of highly dominating convection.