## An error estimate for finite volume methods for multidimensional conservation laws

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- by Bernardo Cockburn, Frédéric Coquel and Philippe LeFloch PDF
- Math. Comp.
**63**(1994), 77-103 Request permission

## 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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## Additional Information

- © Copyright 1994 American Mathematical Society
- 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