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

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Lass_0-310049.pdf
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2015

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http://nbn-resolving.de/urn:nbn:de:bsz:352-0-310049
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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.

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Fachgebiet (DDC)
510 Mathematik

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

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ISO 690LASS, 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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