Residual a posteriori error estimates for two-level finite element methodsfor the Navier-Stokes equations

Residual based a posteriori error estimates for conforming finite element s olutions of the incompressible Navier-Stokes equations which are computed w ith four recently proposed two-level methods are derived. The a posteriori error estimates contain additional terms in comparison to the estimates for the solution obtained by the standard one-level method. The importance of these additional terms in the error estimates is investigated by studying t heir asymptotic behaviour. For optimally scaled meshes, these bounds are no t of higher order than the order of convergence of the discrete solution. ( C) 2001 IMACS. Published by Elsevier Science B.V. All rights reserved.