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Semigroup stability of finite difference schemes for multidimensional hyperbolic initial-boundary value problems


Authors: Jean-François Coulombel and Antoine Gloria
Journal: Math. Comp. 80 (2011), 165-203
MSC (2010): Primary 65M12; Secondary 65M06, 35L50
DOI: https://doi.org/10.1090/S0025-5718-10-02368-9
Published electronically: April 23, 2010
MathSciNet review: 2728976
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Abstract: We develop a simple energy method for proving the stability of finite difference schemes for multidimensional hyperbolic initial-boundary value problems. In particular, we extend to several space dimensions and to variable coefficients a crucial stability result by Goldberg and Tadmor for Dirichlet boundary conditions. This allows us to give some conditions on the discretized operator that ensure that stability estimates for zero initial data imply a semigroup stability estimate for general initial data. We apply this criterion to several numerical schemes in two space dimensions.


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Additional Information

Jean-François Coulombel
Affiliation: CNRS, Université Lille 1 and Team Project SIMPAF of INRIA Lille - Nord Europe, Laboratoire Paul Painlevé (UMR CNRS 8524), Bâtiment M2, Cité Scientifique, 59655 Villeneuve d’Ascq Cedex, France
Email: jean-francois.coulombel@math.univ-lille1.fr

Antoine Gloria
Affiliation: Team Project SIMPAF of INRIA Lille - Nord Europe, Park Plazza, 40 avenue Halley, 59655 Villeneuve d’Ascq Cedex, France
Email: antoine.gloria@inria.fr

DOI: https://doi.org/10.1090/S0025-5718-10-02368-9
Received by editor(s): May 13, 2009
Received by editor(s) in revised form: August 13, 2009, and October 1, 2009
Published electronically: April 23, 2010
Additional Notes: The research of the first author was supported by the Agence Nationale de la Recherche, contract ANR-08-JCJC-0132-01.
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.