Geodesic
Stability of finite difference schemes for hyperbolic initial boundary value problems II
Coulombel, Jean-François1
1CNRS & 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

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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.

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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 
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/
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     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},
     year = {2011},
     publisher = {Scuola Normale Superiore, Pisa},
     volume = {Ser. 5, 10},
     number = {1},
     mrnumber = {2829318},
     zbl = {1225.65089},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ASNSP_2011_5_10_1_37_0/}
}
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