This paper is devoted to the streamline diffusion finite element method, 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 ε, for proper convection vector fields. The key to the estimates is an improved "streamline" Poincaré-Friedrichs inequality.
- Poincaré-Friedrichs inequality
- Robust preconditioning
- Streamline diffusion finite element method
ASJC Scopus subject areas
- Numerical Analysis
- Computational Mathematics
- Applied Mathematics