A posteriori error estimation for a PDE-constrained optimization problem involving the generalized Oseen equations

Allendes, Alejandro and Otárola, Enrique and Rankin, Richard (2018) A posteriori error estimation for a PDE-constrained optimization problem involving the generalized Oseen equations. SIAM Journal on Scientific Computing, 40 (4). A2200-A2233. ISSN 1095-7197

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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.

Item Type: Article
Keywords: linear–quadratic optimal control problems; generalized Oseen equations; Brinkman equations; Stokes equations; a posteriori error estimators; stabilized adaptive finite element methods
Schools/Departments: University of Nottingham Ningbo China > Faculty of Science and Engineering > School of Mathematical Sciences
Identification Number: https://doi.org/10.1137/17M1139631
Depositing User: QIU, Lulu
Date Deposited: 22 Oct 2018 14:41
Last Modified: 22 Oct 2018 14:41
URI: http://eprints.nottingham.ac.uk/id/eprint/55378

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