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Model Reduction by Adaptive Discretization in Optimal Control

  • Rolf RannacherEmail author
Chapter
Part of the International Series of Numerical Mathematics book series (ISNM, volume 165)

Abstract

This article gives a survey of recent developments in the economical numerical solution of PDE-based optimal control problems by adaptive methods. Systematic mesh adaptivity combined with adaptive stopping criteria for linear and nonlinear algebraic iterations is one approach to reducing the computational cost to an acceptable level. These various steps of adaptivity are driven by “goal-oriented” a posteriori error estimates derived within the general framework of the DWR (Dual Weighted Residual) method. The presented material is mainly based on results obtained within the second funding period 2011–2013 of this subproject of the DFG Priority Program 1253 “Optimization with Partial Differential Equations”. In this sense it is the continuation of the article “A posteriori error estimation in PDE-constrained optimization with pointwise inequality constraints” by R. Rannacher, B. Vexler, and W. Wollner in “Constrained Optimization and Optimal Control for Partial Differential Equations” (G. Leugering et al., eds), Birkhüser, Basel, 2012.

Keywords

PDE-based optimization Model reduction Adaptive discretization A posteriori error estimation Goal-oriented adaptivity DWR method Adaptive stopping criteria 

Mathematics Subject Classification (2010)

Primary 35B37 49J20 49M05 49M15 49M29 Secondary 65K10 65M50 65M60 65N22 65N30 65N50 

Notes

Acknowledgements

This work was supported during the period 2007–2013 within the DFG Priority Program 1253 “Optimization with Partial Differential Equations”, grant 306/15-1, “Model reduction by adaptive discretization in optimal control”.

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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  1. 1.Institut für angewandte MathematikUniversität HeidelbergHeidelbergGermany

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