How not to discretize the control
  In this short note, we address the discretization of optimal control problems with higher order polynomials. We develop a necessary and sufficient condition to ensure that weak limits of discrete feasible controls are feasible for the original problem. We show by means of a simple counterexample that a naive discretization by higher order polynomials can lead to non-feasible limits of sequences of discrete solutions. 
Daniel Wachsmuth and Gerd Wachsmuth
math.NA math.OC