Error estimate for the upwind finite volume method for the nonlinear scalar conservation law
type: Item
instance of: scholarly article
title: Error estimate for the upwind finite volume method for the nonlinear scalar conservation law
zbMATH Open document ID: 1227.65078
author: D. Bouche
author: Jean-Michel Ghidaglia
author: Frédéric Pascal
published in: Journal of Computational and Applied Mathematics
publication date: 2011-10-10T00:00:00Z
review text: The error of upwind first order finite volume schemes is estimated and applied to scalar conservation laws. As the first step, the authors consider standard upwind and flux finite volume scheme discretization of a linear equation with space variable coefficients in conservation form. It is proven that, in spite of their lack of consistency, both schemes lead to a first order error estimate. As a final step, a similar estimate for the nonlinear case is proven. The proofs rely on the notion of geometric corrector introduced in a previous paper by the authors [SIAM J. Numer. Anal. 43, No.~2, 578--603 (2005; Zbl 1094.65089)] in the context of constant coefficient linear advection equations.
reviewed by: Ludwig Kohaupt
Mathematics Subject Classification ID: 65M15
Mathematics Subject Classification ID: 65M08
Mathematics Subject Classification ID: 65M12
Mathematics Subject Classification ID: 35L65
zbMATH DE Number: 5955996
zbMATH Keywords: finite volume method
zbMATH Keywords: stability
zbMATH Keywords: convergence
zbMATH Keywords: geometric corrector
zbMATH Keywords: conservation laws
zbMATH Keywords: error estimate
MaRDI profile type: Publication
full work available at URL: j.cam.2011.05.050
OpenAlex ID: W2018234142
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DOI: 10.1016/J.CAM.2011.05.050
description: scientific article; zbMATH DE number 5955996