A simple yet effective a posteriori estimator for classical mixed approximation of Stokes equations

The implementation of quadratic velocity, linear pressure finite element approximation methods for the steady-state incompressible (Navier–)Stokes equations is addressed in this work. Three types of a posteriori error indicator are introduced and are shown to give global error estimates that are equivalent to the true discretisation error. Computational results suggest that the solution of local Poisson problems provides a cost-effective error estimation strategy, both from the perspective of accurate estimation of the global error and for the purpose of selecting elements for refinement within a contemporary self-adaptive refinement algorithm.