A defect-correction method for the incompressible Navier–Stokes equation with a high Reynolds number is considered. In the defect step, the artificial viscosity parameter r is added to the Reynolds number as a stability factor, and the residual is taken care of in the correction step. H 1 and L error estimations are derived for the one-step defectcorrection method, and the results of some numerical experiments are presented. These results show that, for the driven cavity, two defect-correction steps antidiffuse the artificial viscosity approximation nearly optimally. This combination gives on a very coarse mesh, results indistinguishable from a benchmark, very fine mesh calculation. 2002 Elsevier Science Inc. All rights reserved.