We study the stability of the semi-discrete central scheme for the linear damped wave equation with boundary. We exhibit a sufficient condition on the boundary to guarantee the uniform stability of the initial boundary value problem for the relaxation system independently of the stiffness of the source term and of the space step. The boundary is approximated using a summation-by-parts method and the stiff stability is proved using energy estimates and the Laplace transform. We also investigate if the condition is also necessary, following the continuous case studied by Xin and Xu (J. Differ. Equ. 167 (2000) 388–437).
Mots-clés : Hyperbolic relaxation system, damped wave equation, summation by parts operators, central schemes, energy estimates
@article{M2AN_2020__54_5_1569_0,
author = {Boutin, Benjamin and Nguyen, Thi Hoai Thuong and Seguin, Nicolas},
title = {A stiffly stable semi-discrete scheme for the characteristic linear hyperbolic relaxation with boundary},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
pages = {1569--1596},
publisher = {EDP-Sciences},
volume = {54},
number = {5},
year = {2020},
doi = {10.1051/m2an/2020010},
mrnumber = {4127952},
zbl = {1484.65173},
language = {en},
url = {http://www.numdam.org/articles/10.1051/m2an/2020010/}
}
TY - JOUR AU - Boutin, Benjamin AU - Nguyen, Thi Hoai Thuong AU - Seguin, Nicolas TI - A stiffly stable semi-discrete scheme for the characteristic linear hyperbolic relaxation with boundary JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2020 SP - 1569 EP - 1596 VL - 54 IS - 5 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/m2an/2020010/ DO - 10.1051/m2an/2020010 LA - en ID - M2AN_2020__54_5_1569_0 ER -
%0 Journal Article %A Boutin, Benjamin %A Nguyen, Thi Hoai Thuong %A Seguin, Nicolas %T A stiffly stable semi-discrete scheme for the characteristic linear hyperbolic relaxation with boundary %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2020 %P 1569-1596 %V 54 %N 5 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/m2an/2020010/ %R 10.1051/m2an/2020010 %G en %F M2AN_2020__54_5_1569_0
Boutin, Benjamin; Nguyen, Thi Hoai Thuong; Seguin, Nicolas. A stiffly stable semi-discrete scheme for the characteristic linear hyperbolic relaxation with boundary. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 54 (2020) no. 5, pp. 1569-1596. doi : 10.1051/m2an/2020010. http://www.numdam.org/articles/10.1051/m2an/2020010/
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