## Abstract

We derive globally reliable a posteriori error estimators for a linear-quadratic optimal control problem involving the generalized Oseen equations as state equations; control constraints are also considered. The corresponding local error indicators are locally efficient. The assumptions under which we perform the analysis are such that they can be satisfied for a wide variety of stabilized finite element methods as well as for standard finite element methods. When stabilized methods are considered, no a priori relation between the stabilization terms for the state and adjoint equations is required. If a lower bound for the inf-sup constant is available, a posteriori error estimators that are fully computable and provide guaranteed upper bounds on the norm of the error can be obtained. We illustrate the theory with numerical examples.

Original language | English |
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Pages (from-to) | A2200-A2233 |

Journal | SIAM Journal of Scientific Computing |

Volume | 40 |

Issue number | 4 |

DOIs | |

Publication status | Published - 2018 |

## Keywords

- A posteriori error estimators
- Brinkman equations
- Generalized Oseen equations
- Linear-quadratic optimal control problems
- Stabilized adaptive finite element methods
- Stokes equations

## ASJC Scopus subject areas

- Computational Mathematics
- Applied Mathematics