A posteriori error estimation and error control for finite element approximations of the time-dependent Navier-Stokes equations

We present an approach to estimate numerical errors in finite element appro ximations of the time-dependent Navier-Stokes equations along with a strate gy to control these errors. The error estimators and the error control proc edure are based on the residuals of the Navier-Stokes equations, which are shown to be comparable to error components in the velocity variable. The pr esent methodology applies to the estimation of: numerical errors due to the spatial discretization only. Its performance is demonstrated for two-dimen sional:channel flows past a cylinder in the periodic regime. (C) 1999 Elsev ier Science B.V. All rights reserved.