Galerkin proper orthogonal decomposition methods for parameter dependent elliptic systems

• Autorzy: Martin Kahlbacher , Stefan Volkwein
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

proper orthogonal decomposition; elliptic equations; error estimates

Kategorie tematyczne

• 65Kxx: Mathematical programming, optimization and variational techniques
• 35Jxx: Elliptic equations and systems
• 65Nxx: Partial differential equations, boundary value problems

• Wydawca: Faculty of Mathematics, Computer Science and Econometrics, University of Zielona Góra
• Czasopismo: Discussiones Mathematicae, Differential Inclusions, Control and Optimization
• Rocznik: 2007
• Tom: 27
• Numer: 1
• Strony: 95-117

Daty

wydano

2007

otrzymano

2006-03-06

Twórcy

autor

Martin Kahlbacher

• Institute for Mathematics and Scientific Computing, University of Graz, Heinrichstrasse 36, 8010 Graz, Austria

autor

Stefan Volkwein

• Institute for Mathematics and Scientific Computing, University of Graz, Heinrichstrasse 36, 8010 Graz, Austria

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Identyfikatory

DOI

10.7151/dmdico1078