A posteriori error estimates of stabilization of low-order mixed finite elements for incompressible flow

In this paper, we derive a posteriori error estimates for the stabilization of low-order mixed finite element methods for the Stokes equations. By defining different projection estimators, we prove that, up to higher order perturbation terms, the estimators yield global upper and lower bounds on the error of stabilized finite element methods. In numerical tests, each error estimator is shown to be equivalent to the discretization error. It is also shown that the adaptive strategy based on both projection estimators is efficient to detect local singularities in the flow problems.