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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

Error estimate for the approximation of nonlinear conservation laws on bounded domains by the finite volume method


Authors: Mario Ohlberger and Julien Vovelle
Journal: Math. Comp. 75 (2006), 113-150
MSC (2000): Primary 35L65, 65N15
Published electronically: August 12, 2005
MathSciNet review: 2176392
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Abstract: In this paper we derive a priori and a posteriori error estimates for cell centered finite volume approximations of nonlinear conservation laws on polygonal bounded domains. Numerical experiments show the applicability of the a posteriori result for the derivation of local adaptive solution strategies.


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Additional Information

Mario Ohlberger
Affiliation: Abteilung für Angewandte Mathematik, Universität Freiburg, Hermann-Herder-Str.10, D-79104 Freiburg, Germany
Email: mario@mathematik.uni-freibrug.de

Julien Vovelle
Affiliation: Universite de Provence, CMI, F-13453 Marseille, France
Email: vovelle@cmi.univ-mrs.fr

DOI: http://dx.doi.org/10.1090/S0025-5718-05-01770-9
PII: S 0025-5718(05)01770-9
Keywords: Hyperbolic equation, initial boundary value problem, finite volume method, error estimate
Received by editor(s): January 12, 2004
Received by editor(s) in revised form: September 9, 2004
Published electronically: August 12, 2005
Article copyright: © Copyright 2005 American Mathematical Society