Robust preconditioning estimates for convection-dominated elliptic problems via a streamline Poincaré-Friedrichs inequality

This paper is devoted to the streamline diffusion finite element method (SD-FEM), combined with equivalent preconditioning, for solving convection-dominated elliptic problems. The preconditioner is obtained from the streamline diffusion inner product. It is proved that the obtained convergence is robust, i.e. bounded independently of the perturbation parameter epsilon, for proper convection vector fields. The key to the estimates is an improved "streamline" Poincaré-Friedrichs inequality