  Aims. We wish to establish a firm link between jet simulations and analytical
studies of magnetically-driven steady-state jets from Keplerian accretion
disks. In particular, the latter have predicted the existence of recollimation
shocks due to the dominant hoop-stress, so far never observed in platform
simulations.
  Methods. We perform a set of axisymmetric MHD simulations of non-relativistic
jets using the PLUTO code. The simulations are designed to reproduce the
boundary conditions generally expected in analytical studies. We vary two
parameters: the magnetic flux radial exponent $\alpha$ and the jet mass load
$\kappa$. In order to reach the huge unprecedented spatial scales implied by
the analytical solutions, a new method allowing to boost the temporal evolution
has been used.
  Results. We confirm the existence of standing recollimation shocks at large
distances, behaving qualitatively with the mass load $\kappa$ as in
self-similar studies. The shocks are weak and correspond to oblique shocks in a
moderately high fast-magnetosonic flow. The jet emitted from the disk is
focused towards the axial inner spine, which is the outflow connected to the
central objet. The presence of this spine is shown to have a strong influence
on jet asymptotics.
  Conclusions. Internal recollimation shocks may produce observable features
such as standing knots of enhanced emission and a decrease of the flow rotation
rate. However, more realistic simulations, e.g. fully three-dimensional, must
be done in order to investigate non-axisymmetric instabilities and with
ejection only from a finite zone in the disk, so as to to verify whether these
MHD recollimation shocks and their properties are maintained.
