  We introduce a family of mixed methods and discontinuous Galerkin
discretisations designed to numerically solve the Oseen equations written in
terms of velocity, vorticity, and Bernoulli pressure. The unique solvability of
the continuous problem is addressed by invoking a global inf-sup property in an
adequate abstract setting for non-symmetric systems. The proposed finite
element schemes, which produce exactly divergence-free discrete velocities, are
shown to be well-defined and optimal convergence rates are derived in suitable
norms. In addition, we establish optimal rates of convergence for a class of
discontinuous Galerkin schemes, which employ stabilisation. A set of numerical
examples serves to illustrate salient features of these methods.
