Adaptive finite element methods for PDE-constrained optimal control problems

• Verfasst von: Becker, Roland [VerfasserIn]
• Verfasst von: Braack, Malte [VerfasserIn]
• Verfasst von: Meidner, Dominik [VerfasserIn]
• Verfasst von: Rannacher, Rolf [VerfasserIn]
• Titel: Adaptive finite element methods for PDE-constrained optimal control problems
• Verf.angabe: R. Becker, M. Braack, D. Meidner, R. Rannacher, and B. Vexler
• Umfang: 29 S.
• Fussnoten: Gesehen am 11.06.2018
• Titel Quelle: Enthalten in: Reactive flows, diffusion and transport
• Jahr Quelle: 2007
• Band/Heft Quelle: (2007), S. 177-205
• ISBN Quelle: 978-3-540-28396-6
• DOI: doi:10.1007/978-3-540-28396-6_8
• Datenträger: Online-Ressource
• Sprache: eng
• K10plus-PPN: 1576225488

Abstract

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 thoughts A general framework for a posteriori error estimation Solution process and mesh adaptation Examples of optimal control problems Conclusion and outlook References