  We propose a finite element discretization for the steady, generalized
Navier-Stokes equations for fluids with shear-dependent viscosity, completed
with inhomogeneous Dirichlet boundary conditions and an inhomogeneous
divergence constraint. We establish (weak) convergence of discrete solutions as
well as a priori error estimates for the velocity vector field and the scalar
kinematic pressure. Numerical experiments complement the theoretical findings.
