Formation control of autonomous agents can be seen as a physical system of individuals interacting with local potentials, and whose evolution can be described by a Lagrangian function. In this paper, we construct and implement forced variational integrators for the formation control of autonomous agents modeled by double integrators. In particular, we provide an accurate numerical integrator with a lower computational cost than traditional solutions. We find error estimations for the rate of the energy dissipated along with the agents' motion to achieve desired formations. Consequently, this permits to provide sufficient conditions on the simulation's time step for the convergence of discrete formation control systems such as the consensus problem in discrete systems. We present practical applications such as the rapid estimation of regions of attraction to desired shapes in distance-based formation control.