Crank-Nicolson Schemes for Optimal Control Problems with Evolution Equations

@article{Apel2012CrankNicolsonSF,
  title={Crank-Nicolson Schemes for Optimal Control Problems with Evolution Equations},
  author={Thomas Apel and Thomas G. Flaig},
  journal={SIAM J. Numer. Anal.},
  year={2012},
  volume={50},
  pages={1484-1512}
}
  • T. Apel, T. Flaig
  • Published 5 June 2012
  • Mathematics, Computer Science
  • SIAM J. Numer. Anal.
Crank--Nicolson methods are often used for the simulation of initial boundary value problems for parabolic partial differential equations. In this paper we present a family of discretizations for parabolic optimal control problems based on Crank--Nicolson schemes with different time discretizations for state $y$ and adjoint state $p$ so that discretization and optimization commute. One of these methods can also be explained as a Stormer--Verlet scheme in the context of geometric numerical… 
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