Why nonconservative schemes converge to wrong solutions: Error analysis.

*(English)*Zbl 0809.65102The authors study numerical error estimates of nonconservative difference schemes for scalar hyperbolic conservation laws. They obtain a limit equation with a Borel measure source term associated with the nonconservative scheme and an estimate of the error due to nonconservation. Some local correction of such schemes is proposed, so that their convergence to the exact weak solution of the problem can be guaranteed. Many numerical results are provided.

Reviewer: S.Gocheva-Ilieva (Plovdiv)

##### MSC:

65N06 | Finite difference methods for boundary value problems involving PDEs |

65N12 | Stability and convergence of numerical methods for boundary value problems involving PDEs |

65N15 | Error bounds for boundary value problems involving PDEs |

35L65 | Hyperbolic conservation laws |

##### Keywords:

entropy discontinuous solution; error estimates; nonconservative difference schemes; hyperbolic conservation laws; convergence; numerical results
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\textit{T. Y. Hou} and \textit{P. G. Le Floch}, Math. Comput. 62, No. 206, 497--530 (1994; Zbl 0809.65102)

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##### References:

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