  Based on the Uzawa algorithm, we consider an adaptive finite element method
for the Stokes system. We prove linear convergence with optimal algebraic rates
for the residual estimator (which is equivalent to the total error), if the
arising linear systems are solved iteratively, e.g., by PCG. Our analysis
avoids the use of discrete efficiency of the estimator. Unlike prior work, our
adaptive Uzawa algorithm can thus avoid to discretize the given data and does
not rely on an interior node property for the refinement.
