Geodesic
Stability of finite difference schemes for hyperbolic initial boundary value problems II
Coulombel, Jean-François1
1 CNRS & Université Lille 1 Laboratoire Paul Painlevé (UMR CNRS 8524) and Project Team SIMPAF of INRIA Lille Nord Europe Cité scientifique Bâtiment M2 59655 VILLENEUVE D’ASCQ Cedex, France
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 10 (2011) no. 1, pp. 37-98

Voir la notice de l'article provenant de la source Numdam

We study the stability of finite difference schemes for hyperbolic initial boundary value problems in one space dimension. Assuming ℓ 2 -stability for the discretization of the hyperbolic operator as well as a geometric regularity condition, we show that the uniform Kreiss-Lopatinskii condition yields strong stability for the discretized initial boundary value problem. The present work extends the results of [4,7] to the widest possible class of finite difference schemes by dropping the technical assumptions of our former work [4]. We give some new examples of numerical schemes for which our results apply.

Publié le :
Classification : 65M12, 65M06, 35L50

Coulombel, Jean-François 1

1 CNRS & Université Lille 1 Laboratoire Paul Painlevé (UMR CNRS 8524) and Project Team SIMPAF of INRIA Lille Nord Europe Cité scientifique Bâtiment M2 59655 VILLENEUVE D’ASCQ Cedex, France 
@article{ASNSP_2011_5_10_1_37_0,
     author = {Coulombel, Jean-Fran\c{c}ois},
     title = {Stability of finite difference schemes for hyperbolic initial boundary value problems {II}},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
     pages = {37--98},
     publisher = {Scuola Normale Superiore, Pisa},
     volume = {Ser. 5, 10},
     number = {1},
     year = {2011},
     mrnumber = {2829318},
     zbl = {1225.65089},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ASNSP_2011_5_10_1_37_0/}
}
TY  - JOUR
AU  - Coulombel, Jean-François
TI  - Stability of finite difference schemes for hyperbolic initial boundary value problems II
JO  - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY  - 2011
SP  - 37
EP  - 98
VL  - 10
IS  - 1
PB  - Scuola Normale Superiore, Pisa
UR  - http://geodesic.mathdoc.fr/item/ASNSP_2011_5_10_1_37_0/
LA  - en
ID  - ASNSP_2011_5_10_1_37_0
ER  - 
%0 Journal Article
%A Coulombel, Jean-François
%T Stability of finite difference schemes for hyperbolic initial boundary value problems II
%J Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
%D 2011
%P 37-98
%V 10
%N 1
%I Scuola Normale Superiore, Pisa
%U http://geodesic.mathdoc.fr/item/ASNSP_2011_5_10_1_37_0/
%G en
%F ASNSP_2011_5_10_1_37_0
Coulombel, Jean-François. Stability of finite difference schemes for hyperbolic initial boundary value problems II. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 10 (2011) no. 1, pp. 37-98. http://geodesic.mathdoc.fr/item/ASNSP_2011_5_10_1_37_0/