Galerkin proper orthogonal decomposition methods for parameter dependent elliptic systems

Martin Kahlbacher; Stefan Volkwein

Discussiones Mathematicae, Differential Inclusions, Control and Optimization (2007)

  • Volume: 27, Issue: 1, page 95-117
  • ISSN: 1509-9407

Abstract

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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.

How to cite

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Martin Kahlbacher, and Stefan Volkwein. "Galerkin proper orthogonal decomposition methods for parameter dependent elliptic systems." Discussiones Mathematicae, Differential Inclusions, Control and Optimization 27.1 (2007): 95-117. <http://eudml.org/doc/271156>.

@article{MartinKahlbacher2007,
abstract = {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.},
author = {Martin Kahlbacher, Stefan Volkwein},
journal = {Discussiones Mathematicae, Differential Inclusions, Control and Optimization},
keywords = {proper orthogonal decomposition; elliptic equations; error estimates},
language = {eng},
number = {1},
pages = {95-117},
title = {Galerkin proper orthogonal decomposition methods for parameter dependent elliptic systems},
url = {http://eudml.org/doc/271156},
volume = {27},
year = {2007},
}

TY - JOUR
AU - Martin Kahlbacher
AU - Stefan Volkwein
TI - Galerkin proper orthogonal decomposition methods for parameter dependent elliptic systems
JO - Discussiones Mathematicae, Differential Inclusions, Control and Optimization
PY - 2007
VL - 27
IS - 1
SP - 95
EP - 117
AB - 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.
LA - eng
KW - proper orthogonal decomposition; elliptic equations; error estimates
UR - http://eudml.org/doc/271156
ER -

References

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Citations in EuDML Documents

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  1. Dominique Chapelle, Asven Gariah, Jacques Sainte-Marie, Galerkin approximation with proper orthogonal decomposition : new error estimates and illustrative examples
  2. Dominique Chapelle, Asven Gariah, Jacques Sainte-Marie, Galerkin approximation with proper orthogonal decomposition : new error estimates and illustrative examples
  3. Dominique Chapelle, Asven Gariah, Jacques Sainte-Marie, Galerkin approximation with proper orthogonal decomposition : new error estimates and illustrative examples

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