SUMMARYThis paper describes a strategy to control errors in ÿnite element approximations of the time-dependent incompressible Navier-Stokes equations. The approach involves estimating the errors due to the discretization in space, using information from the residuals in the momentum and continuity equations. Following a numerical stability analysis of channel ows past a cylinder, it is concluded that the errors due to the residual in the continuity equation should be carefully controlled since it appears to be the source of unphysical perturbations artiÿcially created by the spatial discretization. The performance of the adaptive strategy is then tested for lid-driven oblique cavity ows.