A robust a posteriori error estimator for the Oseen problem

Abstract

A residual-based a posteriori error estimator is proposed for the incompressible Oseen problem in the convection-dominated regime. The SUPG/PSPG/grad-div stabilized finite element method is used as discretization. The error estimator estimates the global error in a norm that is used in the a priori error analysis of the method. Based on several hypotheses concerning the error and interpolation errors, the robustness of the estimator in the convection-dominated regime is proved. Numerical studies support the analytic results. Finally, the extension of the a posteriori error estimator to the steady-state Navier--Stokes equations is discussed.