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A note on entropy inequalities and error estimates for higher-order accurate finite volume schemes on irregular families of grids

Author: Sebastian Noelle
Journal: Math. Comp. 65 (1996), 1155-1163
MSC (1991): Primary 35L65, 65M12, 65M15, 65M50
MathSciNet review: 1344618
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Abstract: Recently, Cockburn, Coquel and LeFloch proved convergence and error estimates for higher-order finite volume schemes. Their result is based on entropy inequalities which are derived under restrictive assumptions on either the flux function or the numerical fluxes. Moreover, they assume that the spatial grid satisfies a standard regularity assumption. Using instead entropy inequalities derived in previous work by Kröner, Noelle and Rokyta and a weaker condition on the grid, we can generalize and simplify the error estimates.

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Additional Information

Sebastian Noelle

Keywords: Multidimensional conservation law, finite volume method, discrete entropy inequality, error estimate, irregular grids
Received by editor(s): March 21, 1995
Additional Notes: Partially supported by Deutsche Forschungsgemeinschaft, SFB 256.
Article copyright: © Copyright 1996 American Mathematical Society