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.
Mots-clés : model order reduction, proper orthogonal decomposition, wave equation
@article{M2AN_2014__48_1_135_0,
author = {Amsallem, D. and Hetmaniuk, U.},
title = {Error estimates for {Galerkin} reduced-order models of the semi-discrete wave equation},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
pages = {135--163},
publisher = {EDP-Sciences},
volume = {48},
number = {1},
year = {2014},
doi = {10.1051/m2an/2013099},
mrnumber = {3177840},
zbl = {1290.65087},
language = {en},
url = {http://archive.numdam.org/articles/10.1051/m2an/2013099/}
}
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 PY - 2014 SP - 135 EP - 163 VL - 48 IS - 1 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/m2an/2013099/ DO - 10.1051/m2an/2013099 LA - en ID - M2AN_2014__48_1_135_0 ER -
%0 Journal Article %A Amsallem, D. %A Hetmaniuk, U. %T Error estimates for Galerkin reduced-order models of the semi-discrete wave equation %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2014 %P 135-163 %V 48 %N 1 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/m2an/2013099/ %R 10.1051/m2an/2013099 %G en %F M2AN_2014__48_1_135_0
Amsallem, D.; Hetmaniuk, U. Error estimates for Galerkin reduced-order models of the semi-discrete wave equation. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 48 (2014) no. 1, pp. 135-163. doi : 10.1051/m2an/2013099. http://archive.numdam.org/articles/10.1051/m2an/2013099/
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