We propose a generalized finite element method for the strongly damped wave equation with highly varying coefficients. The proposed method is based on the localized orthogonal decomposition introduced in Målqvist and Peterseim [Math. Comp. 83 (2014) 2583–2603], and is designed to handle independent variations in both the damping and the wave propagation speed respectively. The method does so by automatically correcting for the damping in the transient phase and for the propagation speed in the steady state phase. Convergence of optimal order is proven in L2(H1)-norm, independent of the derivatives of the coefficients. We present numerical examples that confirm the theoretical findings.
Accepté le :
Publié le :
DOI : 10.1051/m2an/2021023
Keywords: Strongly damped wave equation, multiscale, localized orthogonal decomposition, finite element method, reduced basis method
@article{M2AN_2021__55_4_1375_0,
author = {Ljung, Per and M\r{a}lqvist, Axel and Persson, Anna},
title = {A generalized finite element method for the strongly damped wave equation with rapidly varying data},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
pages = {1375--1404},
year = {2021},
publisher = {EDP-Sciences},
volume = {55},
number = {4},
doi = {10.1051/m2an/2021023},
mrnumber = {4281738},
zbl = {07523502},
language = {en},
url = {https://www.numdam.org/articles/10.1051/m2an/2021023/}
}
TY - JOUR AU - Ljung, Per AU - Målqvist, Axel AU - Persson, Anna TI - A generalized finite element method for the strongly damped wave equation with rapidly varying data JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2021 SP - 1375 EP - 1404 VL - 55 IS - 4 PB - EDP-Sciences UR - https://www.numdam.org/articles/10.1051/m2an/2021023/ DO - 10.1051/m2an/2021023 LA - en ID - M2AN_2021__55_4_1375_0 ER -
%0 Journal Article %A Ljung, Per %A Målqvist, Axel %A Persson, Anna %T A generalized finite element method for the strongly damped wave equation with rapidly varying data %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2021 %P 1375-1404 %V 55 %N 4 %I EDP-Sciences %U https://www.numdam.org/articles/10.1051/m2an/2021023/ %R 10.1051/m2an/2021023 %G en %F M2AN_2021__55_4_1375_0
Ljung, Per; Målqvist, Axel; Persson, Anna. A generalized finite element method for the strongly damped wave equation with rapidly varying data. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 55 (2021) no. 4, pp. 1375-1404. doi: 10.1051/m2an/2021023
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