In this paper we apply the recently developed mimetic discretization method
[44] to the mixed formulation of the Stokes problem in terms of the
vorticity-velocity-pressure formulation. The mimetic discretization presented
in this paper and in [44] is a higher-order method for curvilinear
quadrilaterals. It relies on the language of differential $k$-forms,
$k$-cochains as its discrete counterpart, and the relations between them in
terms of the mimetic operators: reduction, reconstruction and projection. The
reconstruction consists of a mimetic spectral element method. The most
important result of the mimetic framework is the commutation between
differentiation at the continuous level with that on the finite dimensional and
discrete level. As a result operators like gradient, curl and divergence are
discretized exactly. For Stokes flow, this implies a pointwise divergence-free
solution. This is confirmed using a set of test cases on both Cartesian and
curvilinear meshes. It will be shown that the method preforms optimally for all
admissible boundary conditions.