Error analysis of variational integrators of unconstrained Lagrangian   systems
  A complete error analysis of variational integrators is obtained, by blowing up the discrete variational principles, all of which have a singularity at zero time-step. Divisions by the time step lead to an order that is one less than observed in simulations, a deficit that is repaired with the help of a new past-future symmetry. 
George W. Patrick and Charles Cuell