Discrete calculus of variations for quadratic lagrangians
  We develop in this paper a new framework for discrete calculus of variations when the actions have densities involving an arbitrary discretization operator. We deduce the discrete Euler-Lagrange equations for piecewise continuous critical points of sampled actions. Then we characterize the discretization operators such that, for all quadratic lagrangian, the discrete Euler-Lagrange equations converge to the classical ones. 
Philippe Ryckelynck and Laurent Smoch
math.OC cs.SY