An error estimate for finite volume methods for multidimensional conservation laws

Cockburn, Bernardo; Coquel, Frédéric; LeFloch, Philippe

doi:10.1090/S0025-5718-1994-1240657-4

An error estimate for finite volume methods for multidimensional conservation laws

Authors: Bernardo Cockburn, Frédéric Coquel and Philippe LeFloch
Journal: Math. Comp. 63 (1994), 77-103
MSC: Primary 65M15; Secondary 35L65, 65M60
DOI: https://doi.org/10.1090/S0025-5718-1994-1240657-4
MathSciNet review: 1240657
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Abstract: In this paper, an ${L^\infty }({L^1})$ -error estimate for a class of finite volume methods for the approximation of scalar multidimensional conservation laws is obtained. These methods can be formally high-order accurate and are defined on general triangulations. The error is proven to be of order ${h^{1/4}}$ , where h represents the "size" of the mesh, via an extension of Kuznetsov approximation theory for which no estimate of the total variation and of the modulus of continuity in time are needed. The result is new even for the finite volume method constructed from monotone numerical flux functions.

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