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

 

A posteriori error estimates
for upwind finite volume schemes
for nonlinear conservation laws
in multi dimensions


Authors: Dietmar Kröner and Mario Ohlberger
Journal: Math. Comp. 69 (2000), 25-39
MSC (1991): Primary 65M15, 35L65, 76M25
Published electronically: August 18, 1999
MathSciNet review: 1659843
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Abstract | References | Similar Articles | Additional Information

Abstract: In this paper we shall derive a posteriori error estimates in the $L^1$-norm for upwind finite volume schemes for the discretization of nonlinear conservation laws on unstructured grids in multi dimensions. This result is mainly based on some fundamental a priori error estimates published in a recent paper by C. Chainais-Hillairet. The theoretical results are confirmed by numerical experiments.


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Additional Information

Dietmar Kröner
Affiliation: Institut für Angewandte Mathematik, Universität Freiburg, Herrmann-Herder-Str. 10, 79104 Freiburg, Germany
Email: dietmar@mathematik.uni-freiburg.de, mario@mathematik.uni-freiburg.de

Mario Ohlberger
Affiliation: Institut für Angewandte Mathematik, Universität Freiburg, Herrmann-Herder-Str. 10, 79104 Freiburg, Germany

DOI: http://dx.doi.org/10.1090/S0025-5718-99-01158-8
PII: S 0025-5718(99)01158-8
Keywords: A posteriori error estimates, conservation laws, finite volume schemes, adaptive methods, unstructured grids
Received by editor(s): February 5, 1998
Published electronically: August 18, 1999
Article copyright: © Copyright 1999 American Mathematical Society