SUMMARYIn the present paper, the author shows that the predictor=multi-corrector (PMC) time integration for the advection-di usion equations induces numerical di usivity acting only in the streamline direction, even though the equations are spatially discretized by the conventional Galerkin ÿnite element method (GFEM). The transient 2-D and 3-D advection problems are solved with the PMC scheme using both the GFEM and the streamline upwind=Petrov Galerkin (SUPG) as the spatial discretization methods for comparison. The solutions of the SUPG-PMC turned out to be overly di usive due to the additional PMC streamline di usion, while the solutions of the GFEM-PMC were comparatively accurate without signiÿcant damping and phase error. A similar tendency was seen also in the quasi-steady solutions to the incompressible viscous ow problems: 2-D driven cavity ow and natural convection in a square cavity.