| Issue |
ESAIM: M2AN
Volume 54, Number 5, September-October 2020
|
|
|---|---|---|
| Page(s) | 1569 - 1596 | |
| DOI | https://doi.org/10.1051/m2an/2020010 | |
| Published online | 28 July 2020 | |
A stiffly stable semi-discrete scheme for the characteristic linear hyperbolic relaxation with boundary
IRMAR (UMR CNRS 6625), Université de Rennes, Campus de Beaulieu, 35042 Rennes Cedex, France
* Corresponding author: benjamin.boutin@univ-rennes1.fr
Received:
22
May
2019
Accepted:
11
February
2020
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).
Mathematics Subject Classification: 35F46 / 35L50 / 65M06 / 65M12
Key words: Hyperbolic relaxation system / damped wave equation / summation by parts operators / central schemes / energy estimates
© The authors. Published by EDP Sciences, SMAI 2020
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