Residual a posteriori error estimates for two-level finite element methods for the Navier–Stokes equations Original Research Article

Residual based a posteriori error estimates for conforming finite element solutions of the incompressible Navier–Stokes equations which are computed with 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 their asymptotic behaviour. For optimally scaled meshes, these bounds are not of higher order than the order of convergence of the discrete solution.