# Error estimates for Galerkin reduced-order models of the semi-discrete wave equation

- Volume: 48, Issue: 1, page 135-163
- ISSN: 0764-583X

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topAmsallem, D., and Hetmaniuk, U.. "Error estimates for Galerkin reduced-order models of the semi-discrete wave equation." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 48.1 (2014): 135-163. <http://eudml.org/doc/273305>.

@article{Amsallem2014,

abstract = {Galerkin reduced-order models for the semi-discrete wave equation, that preserve the second-order structure, are studied. Error bounds for the full state variables are derived in the continuous setting (when the whole trajectory is known) and in the discrete setting when the Newmark average-acceleration scheme is used on the second-order semi-discrete equation. When the approximating subspace is constructed using the proper orthogonal decomposition, the error estimates are proportional to the sums of the neglected singular values. Numerical experiments illustrate the theoretical results.},

author = {Amsallem, D., Hetmaniuk, U.},

journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},

keywords = {model order reduction; proper orthogonal decomposition; wave equation; Galerkin reduced-order models; Newmark schemes; second-order structure preservation; convergence acceleration; semidiscretization; error estimates; numerical experiments},

language = {eng},

number = {1},

pages = {135-163},

publisher = {EDP-Sciences},

title = {Error estimates for Galerkin reduced-order models of the semi-discrete wave equation},

url = {http://eudml.org/doc/273305},

volume = {48},

year = {2014},

}

TY - JOUR

AU - Amsallem, D.

AU - Hetmaniuk, U.

TI - Error estimates for Galerkin reduced-order models of the semi-discrete wave equation

JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

PY - 2014

PB - EDP-Sciences

VL - 48

IS - 1

SP - 135

EP - 163

AB - Galerkin reduced-order models for the semi-discrete wave equation, that preserve the second-order structure, are studied. Error bounds for the full state variables are derived in the continuous setting (when the whole trajectory is known) and in the discrete setting when the Newmark average-acceleration scheme is used on the second-order semi-discrete equation. When the approximating subspace is constructed using the proper orthogonal decomposition, the error estimates are proportional to the sums of the neglected singular values. Numerical experiments illustrate the theoretical results.

LA - eng

KW - model order reduction; proper orthogonal decomposition; wave equation; Galerkin reduced-order models; Newmark schemes; second-order structure preservation; convergence acceleration; semidiscretization; error estimates; numerical experiments

UR - http://eudml.org/doc/273305

ER -

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