A flux-free a posteriori error estimator for the incompressible Stokes problem using a mixed FE formulation

In this contribution, we present an a posteriori error estimator for the incompressible Stokes problem valid for a conventional mixed FE formulation Due to the saddle-point property of the problem, conventional error estimators developed for pure minimization problems cannot be utilized straight-forwardly The new estimator is built up by two key ingredients At first, a computed error approximation, exactly fulfilling the continuity equation for the error, is obtained via local Dirichlet problems Secondly, we adopt the approach of solving local equilibrated flux-free problems in order to bound the remaining, incompressible, error In this manner, guaranteed upper and lower bounds, of the velocity "energy norm" of the error as well as goal-oriented (linear) output functionals, with respect to a reference (overkill) mesh are obtained In particular, it should be noted that this approach requires no computation of hybrid fluxes Furthermore, the estimator is applicable to mixed FE formulations using continuous pressure approximations, such as the Mini and Taylor-Hood class of elements. In conclusion, a few simple numerical examples are presented, illustrating the accuracy of the error bounds (C) 2010 Elsevier B V All rights reserve