Computable error bounds for nonconforming Fortin-Soulie finite element approximation of the Stokes problem

We propose computable a posteriori error estimates for a second-order nonconforming finite element approximation of the Stokes problem. The estimator is completely free of unknown constants and gives a guaranteed numerical upper bound on the error in terms of a lower bound for the inf-sup constant of the underlying continuous problem. The estimator is also shown to provide a lower bound on the error up to a constant and higher-order data oscillation terms. Numerical results are presented illustrating the theory and the performance of the estimator.