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Why nonconservative schemes converge to wrong solutions: Error analysis. (English) Zbl 0809.65102
The 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.

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
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