We present mesoscopic simulations of the counterion-induced electro-osmotic flow in different electrostatic coupling regimes. Two simulation methods are compared, dissipative particle dynamics (DPD) and coupled lattice-Boltzmann/molecular dynamics (LB/MD). A general mapping scheme to match DPD to LB/MD is developed. For the weak coupling regime, analytic expressions for the flow profiles in the presence of partial-slip as well as no-slip boundary conditions are derived from the Poisson-Boltzmann and Stokes equations, which are in good agreement with the numerical results. The influence of electrofriction and partial slip on the flow profiles is discussed.