Article

Journal of Scientific Computing

, Volume 56, Issue 1, pp 14-27

First online:

Mimetic Discretizations of Elliptic Control Problems

  • Paola F. AntoniettiAffiliated withMOX, Dipartimento di Matematica, Politecnico di Milano
  • , Nadia BigoniAffiliated withMOX, Dipartimento di Matematica, Politecnico di Milano Email author 
  • , Marco VeraniAffiliated withMOX, Dipartimento di Matematica, Politecnico di Milano

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Abstract

We investigate the performance of the Mimetic Finite Difference (MFD) method for the approximation of a constraint optimal control problem governed by an elliptic operator. Low-order and high-order mimetic discretizations are considered and a priori error estimates are derived, in a suitable discrete norm, for both the control and the state variables. A wide class of numerical experiments performed on a set of examples selected from the literature assesses the robustness of the MFD method and confirms the convergence analysis.

Keywords

Optimal control problems Mimetic finite difference method Mixed formulation