Optimality conditions and POD a-posteriori error estimates for a semilinear parabolic optimal control

Lass, Oliver; Trenz, Stefan; Volkwein, Stefan

Optimality conditions and POD a-posteriori error estimates for a semilinear parabolic optimal control

Dateien

Lass_0-310049.pdfGröße: 1.46 MBDownloads: 217

Datum

2015

Publikationstyp

Working Paper/Technical Report

Publikationsstatus

Published

Zusammenfassung

In the present paper the authors consider an optimal control problem for a parametrized nonlinear parabolic differential equation, which is motivated by lithium-ion battery models. A standard finite element (FE) discretization leads to a large-scale nonlinear optimization problem so that its numerical solution is very costly. Therefore, a reduced-order modelling based on proper orthogonal decomposition (POD) is applied, so that the number of degrees of freedom is reduced significantly and a fast numerical simulation of the model is possible. To control the error, an a-posteriori error estimator is realized. Numerical experiments show the efficiency of the approach.

Fachgebiet (DDC)

510 Mathematik

Schlagwörter

Optimal control, semilinear parabolic differential equations, a-posteriori analysis, proper orthogonal decomposition, projected Newton method

Zitieren

ISO 690

LASS, Oliver, Stefan TRENZ, Stefan VOLKWEIN, 2015. Optimality conditions and POD a-posteriori error estimates for a semilinear parabolic optimal control

BibTex

@techreport{Lass2015Optim-32287,
  year={2015},
  series={Konstanzer Schriften in Mathematik},
  title={Optimality conditions and POD a-posteriori error estimates for a semilinear parabolic optimal control},
  number={345},
  author={Lass, Oliver and Trenz, Stefan and Volkwein, Stefan}
}

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