Highorder schemes and entropy condition for nonlinear hyperbolic systems of conservation laws
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 by J.P. Vila PDF
 Math. Comp. 50 (1988), 5373 Request permission
Abstract:
A systematic procedure for constructing explicit, quasi secondorder approximations to strictly hyperbolic systems of conservation laws is presented. These new schemes are obtained by correcting firstorder schemes. We prove that limit solutions satisfy the entropy inequality. In the scalar case, we prove convergence to the unique entropysatisfying solution if the initial scheme is Total Variation Decreasing (i.e., TVD) and consistent with the entropy condition. Finally, we slightly modify Harten’s highorder schemes such that they obey the previous conditions and thus converge towards the "entropy" solution.References

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Additional Information
 © Copyright 1988 American Mathematical Society
 Journal: Math. Comp. 50 (1988), 5373
 MSC: Primary 65M10; Secondary 35L65
 DOI: https://doi.org/10.1090/S00255718198809178181
 MathSciNet review: 917818