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Galerkin proper orthogonal decomposition methods for parameter dependent elliptic systems

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2007

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Kahlbacher, Martin

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Discussiones Mathematicae / Differential Inclusions, Control and Optimization. 2007, 27(1), pp. 95-117. ISSN 1509-9407. eISSN 2084-0365

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Proper orthogonal decomposition (POD) is a powerful technique for model reduction of linear and non-linear systems. It is based on a Galerkin type discretization with basis elements created from the system itself. In this work, error estimates for Galerkin POD methods for linear elliptic, parameter-dependent systems are proved. The resulting error bounds depend on the number of POD basis functions and on the parameter grid that is used to generate the snapshots and to compute the POD basis. The error estimates also hold for semi-linear elliptic problems with monotone nonlinearity. Numerical examples are included.

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510 Mathematik

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ISO 690KAHLBACHER, Martin, Stefan VOLKWEIN, 2007. Galerkin proper orthogonal decomposition methods for parameter dependent elliptic systems. In: Discussiones Mathematicae / Differential Inclusions, Control and Optimization. 2007, 27(1), pp. 95-117. ISSN 1509-9407. eISSN 2084-0365
BibTex
@article{Kahlbacher2007Galer-41203,
  year={2007},
  title={Galerkin proper orthogonal decomposition methods for parameter dependent elliptic systems},
  number={1},
  volume={27},
  issn={1509-9407},
  journal={Discussiones Mathematicae / Differential Inclusions, Control and Optimization},
  pages={95--117},
  author={Kahlbacher, Martin and Volkwein, Stefan}
}
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