Uniform stability of the SUPG method for the evolutionary convection-diffusion-reaction equation

To solve the evolutionary convection-diffusion-reaction equation, the implicit Euler method and the streamline upwind Petrov Galerkin (SUPG) method are used for time discretization and space discretization respectively in this paper. Uniform stability is obtained with respect to the temporal and spatial discretization parameters. A new projection is introduced for the stability analysis instead of the common idea of material derivative. The analysis does not require a strict relation between time step and space step, which is usually needed by derivations based on the technique of material derivative. Furthermore, it can handle the case of time-dependent convection and reaction coefficients.

Automated summary

The implicit Euler method and the streamline upwind Petrov Galerkin (SUPG) method were used to solve the evolutionary convection-diffusion-reaction equation, obtaining uniform stability with respect to the temporal and spatial discretization parameters. A new projection was introduced for stability analysis instead of the common idea of material derivative, allowing flexibility in the relation between time step and space step. This analysis can also handle time-dependent convection and reaction coefficients.