Title :

Stability of finite difference schemes for hyperbolic initial boundary value problems

Author(s) :

Coulombel, Jean-François [Auteur]
SImulations and Modeling for PArticles and Fluids [SIMPAF]

Journal title :

SIAM Journal on Numerical Analysis

Pages :

2844-2871

Publisher :

Society for Industrial and Applied Mathematics

Publication date :

2009-12-31

ISSN :

0036-1429

English keyword(s) :

finite difference schemes
stability
symmetrizers
Hyperbolic systems
boundary conditions

HAL domain(s) :

Mathématiques [math]/Equations aux dérivées partielles [math.AP]
Mathématiques [math]/Analyse numérique [math.NA]

English abstract : [en]

We study the stability of finite difference schemes for hyperbolic initial boundary value problems in one space dimension. Assuming stability for the dicretization of the hyperbolic operator as well as a geometric regularity ...
Show more >We study the stability of finite difference schemes for hyperbolic initial boundary value problems in one space dimension. Assuming stability for the dicretization of the hyperbolic operator as well as a geometric regularity condition, we show that an appropriate determinant condition, that is the analogue of the uniform Kreiss-Lopatinskii condition for the continuous problem, yields strong stability for the discretized initial boundary value problem. The analysis relies on a suitable discrete block structure condition and the construction of suitable symmetrizers. Our work extends the results of Gustafsson, Kreiss, Sundstrom to a wider class of finite difference schemes.Show less >

Language :

Anglais

Popular science :

Non

Collections :

• Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL