  We prove the contraction property for two successive loops of the adaptive
algorithm for the Stokes problem reducing the error of the velocity. The
problem is discretized by a divergence-conforming discontinuous Galerkin method
which separates pressure and velocity approximation due to its cochain
property. This allows us to establish the quasi-orthogonality property which is
crucial for the proof of the contraction. We also establish the quasi-optimal
complexity of the adaptive algorithm in terms of the degrees of freedom.
