  We approximate the solution of the stationary Stokes equations with various
conforming and nonconforming inf-sup stable pairs of finite element spaces on
simplicial meshes. Based on each pair, we design a discretization that is
quasi-optimal and pressure robust, in the sense that the velocity $H^1$-error
is proportional to the best $H^1$-error to the analytical velocity. This shows
that such a property can be achieved without using conforming and
divergence-free pairs. We bound also the pressure $L^2$-error, only in terms of
the best approximation errors to the analytical velocity and the analytical
pressure. Our construction can be summarized as follows. First, a linear
operator acts on discrete velocity test functions, before the application of
the load functional, and maps the discrete kernel into the analytical one.
Second, in order to enforce consistency, we employ a new augmented Lagrangian
formulation, inspired by Discontinuous Galerkin methods.
