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.
@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 - Mod\'elisation Math\'ematique et Analyse Num\'erique},
volume = {48},
year = {2014},
pages = {135-163},
doi = {10.1051/m2an/2013099},
mrnumber = {3177840},
zbl = {1290.65087},
language = {en},
url = {http://dml.mathdoc.fr/item/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 - Modélisation Mathématique et Analyse Numérique, Tome 48 (2014) pp. 135-163. doi : 10.1051/m2an/2013099. http://gdmltest.u-ga.fr/item/M2AN_2014__48_1_135_0/
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