A-posteriori error estimation of discrete POD models for PDE-constrained optimal control
A-posteriori error estimation of discrete POD models for PDE-constrained optimal control
View/Date of Publication
03.2016Publisher
Institut für Numerische Simulation (INS)Publisher Location
BonnMetadata
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Citable Link (Handle URI) 
https://hdl.handle.net/20.500.11811/11852
Abstract
In this work a-posteriori error estimates for linear-quadratic optimal control problems governed by parabolic equations are considered. Different error estimation techniques for finite element discretizations and model-order reduction are combined to validate suboptimal control solutions from low-order models which are constructed by Galerkin discretization and application of proper orthogonal decomposition (POD). The theoretical findings are used to design an efficient updating algorithm for the reduced-order models; the efficiency and accuracy is illustrated by numerical experiments.
Subjects
Proper Orthogonal Decomposition (POD), Reduced Order Model (ROM), Discretization Error Estimates, Optimal Control Problem, Partial Differential Equations (PDEs)
Classification (DDC)
510 Mathematik 518 Numerische AnalysisFirst Publication
https://ins.uni-bonn.de/publication/preprintsRelated Publications
https://doi.org/10.1007/978-3-319-58786-8_14Part of Series
INS Preprints ; 1608Gubisch, Martin; Neitzel, Ira; Volkwein, Stefan: A-posteriori error estimation of discrete POD models for PDE-constrained optimal control. In: INS Preprints, 1608.
Online-Ausgabe in bonndoc: https://hdl.handle.net/20.500.11811/11852
Online-Ausgabe in bonndoc: https://hdl.handle.net/20.500.11811/11852
@unpublished{handle:20.500.11811/11852,
author = {{Martin Gubisch} and {Ira Neitzel} and {Stefan Volkwein}},
title = {A-posteriori error estimation of discrete POD models for PDE-constrained optimal control},
publisher = {Institut für Numerische Simulation (INS)},
year = 2016,
month = mar,
INS Preprints},
volume = 1608,
note = {In this work a-posteriori error estimates for linear-quadratic optimal control problems governed by parabolic equations are considered. Different error estimation techniques for finite element discretizations and model-order reduction are combined to validate suboptimal control solutions from low-order models which are constructed by Galerkin discretization and application of proper orthogonal decomposition (POD). The theoretical findings are used to design an efficient updating algorithm for the reduced-order models; the efficiency and accuracy is illustrated by numerical experiments.},
url = {https://hdl.handle.net/20.500.11811/11852}
}
author = {{Martin Gubisch} and {Ira Neitzel} and {Stefan Volkwein}},
title = {A-posteriori error estimation of discrete POD models for PDE-constrained optimal control},
publisher = {Institut für Numerische Simulation (INS)},
year = 2016,
month = mar,
INS Preprints},
volume = 1608,
note = {In this work a-posteriori error estimates for linear-quadratic optimal control problems governed by parabolic equations are considered. Different error estimation techniques for finite element discretizations and model-order reduction are combined to validate suboptimal control solutions from low-order models which are constructed by Galerkin discretization and application of proper orthogonal decomposition (POD). The theoretical findings are used to design an efficient updating algorithm for the reduced-order models; the efficiency and accuracy is illustrated by numerical experiments.},
url = {https://hdl.handle.net/20.500.11811/11852}
}
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