Adaptive Finite Element Methods for PDE-Constrained Optimal Control Problems.

We present a systematic approach to error control and mesh adaptation in the numerical solution of optimal control problems governed by partial differential equations. By the Lagrangian formalism the optimization problem is reformulated as a saddle-point boundary value problem which is discretized by a finite element Galerkin method. The accuracy of the discretization is controlled by residual-based a posteriori error estimates. The main features of this method are illustrated by examples from optimal control of heat transfer, fluid flow and parameter estimation. The contents of this article is as follows: Preliminary thoughtsA general framework for a posteriori error estimationSolution process and mesh adaptationExamples of optimal control problemsConclusion and outlookReferences [ABSTRACT FROM AUTHOR]