  The Newtonian simulations describing the formation of large-scale structures
do not include relativistic effects. A new approach to this problem is
proposed, which consists of splitting the Hawking-Hayward quasi-local energy of
a closed spacelike 2-surface into a "Newtonian" part due to local perturbations
and a "relativistic" part due to the cosmology. It is found that the Newtonian
part dominates over the relativistic one as time evolves, lending support to
the validity of Newtonian simulations.
