The streamline diffusion method for time dependent convection: diffusion problems with small diffusion
Abstract
A time stepping version of the streamline diffusion method, previously considered in the case of a stationary convection-diffusion problem with small diffusion, is introduced and analyzed. At each timestep the usual Galerkin method is applied to a modified convection-diffusion problem obtained by adding extra diffusion in the streamline direction (in both time and space) and compensating by modifying the right hand side of the equation. The discrete solution will be continuous in space, but may be discontinuous in time at the discrete time levels. Global and local error estimates are derived, the latter being of interest in the case of a nonsmooth exact solution, and the results of some numerical experiments are reported.
- Publication:
-
NASA STI/Recon Technical Report N
- Pub Date:
- January 1981
- Bibcode:
- 1981STIN...8132470N
- Keywords:
-
- Convective Flow;
- Diffusion;
- Galerkin Method;
- Time Dependence;
- Error Analysis;
- Finite Difference Theory;
- Finite Element Method;
- Time Marching;
- Fluid Mechanics and Heat Transfer