Back to Search
Start Over
A stiffly stable semi-discrete scheme for the characteristic linear hyperbolic relaxation with boundary
A stiffly stable semi-discrete scheme for the characteristic linear hyperbolic relaxation with boundary
- Source :
- ESAIM: Mathematical Modelling and Numerical Analysis, ESAIM: Mathematical Modelling and Numerical Analysis, 2020, 54 (5), pp.1569-1596. ⟨10.1051/m2an/2020010⟩, ESAIM: Mathematical Modelling and Numerical Analysis, EDP Sciences, 2020, 54 (5), pp.1569-1596. ⟨10.1051/m2an/2020010⟩
- Publication Year :
- 2020
- Publisher :
- EDP Sciences, 2020.
-
Abstract
- International audience; 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 relaxation system independent of 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 by energy estimates and Laplace transform. We also investigate if the condition is also necessary, following the continuous case studied by Xin and Xu (2000).; Nous étudions la stabilité du schéma semi-discret centré pour l'équation des ondes linéaire amortie posé sur un demi-espace. Nous dégageons une condition suffisante portant sur la condition de bord, pour la stabilité du problème semi-discret avec donnée initiale et donnée de bord, ceci de manière uniforme par rapport à la raideur du terme source de relaxation ainsi qu'au pas d'espace. La discrétisation de la condition de bord employée provient de l'approche SBP et l'uniforme stabilité s'obtient par l'utilisation de méthodes d'énergie et de la transformée de Laplace. Nous examinons également au travers d'expériences numériques le caractère nécessaire de la condition retenue, de sorte à confronter notre résultat à l'étude de Xin et Xu (2000) portant sur le cas continu.
- Subjects :
- Boundary (topology)
010103 numerical & computational mathematics
summation by parts operators
Space (mathematics)
01 natural sciences
Stability (probability)
010305 fluids & plasmas
central schemes
0103 physical sciences
medicine
[MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP]
damped wave equation
Boundary value problem
0101 mathematics
Mathematics
Numerical Analysis
Laplace transform
energy estimates
Applied Mathematics
Mathematical analysis
Stiffness
Damped wave
Computational Mathematics
Modeling and Simulation
hyperbolic relaxation system
Relaxation (approximation)
medicine.symptom
[MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA]
Analysis
Subjects
Details
- ISSN :
- 12903841 and 0764583X
- Volume :
- 54
- Database :
- OpenAIRE
- Journal :
- ESAIM: Mathematical Modelling and Numerical Analysis
- Accession number :
- edsair.doi.dedup.....3a7b0ee822d88d35530fadb341dfcfdd
- Full Text :
- https://doi.org/10.1051/m2an/2020010