## Abstract

We derive a posteriori error estimators for an optimal control problem governed by a convection–reaction–diffusion equation; control constraints are also considered. We consider a family of low-order stabilized finite element methods to approximate the solutions to the state and adjoint equations. We obtain a fully computable a posteriori error estimator for the optimal control problem. All the constants that appear in the upper bound for the error are fully specified. Therefore, the proposed estimator can be used as a stopping criterion in adaptive algorithms. We also obtain a robust a posteriori error estimator for when the error is measured in a norm that involves the dual norm of the convective derivative. Numerical examples, in two and three dimensions, are presented to illustrate the theory.

Original language | English |
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Pages (from-to) | 147-177 |

Number of pages | 31 |

Journal | Computer Methods in Applied Mechanics and Engineering |

Volume | 340 |

DOIs | |

Publication status | Published - 1 Oct 2018 |

## Keywords

- Convection–reaction–diffusion equation
- Fully computable a posteriori error estimator
- Linear–quadratic optimal control problem
- Robust a posteriori error estimator
- Stabilized methods

## ASJC Scopus subject areas

- Computational Mechanics
- Mechanics of Materials
- Mechanical Engineering
- Physics and Astronomy (all)
- Computer Science Applications