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Mathematics of Computation

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High-order schemes and entropy condition for nonlinear hyperbolic systems of conservation laws

Author: J.-P. Vila
Journal: Math. Comp. 50 (1988), 53-73
MSC: Primary 65M10; Secondary 35L65
MathSciNet review: 917818
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Abstract: A systematic procedure for constructing explicit, quasi second-order approximations to strictly hyperbolic systems of conservation laws is presented. These new schemes are obtained by correcting first-order schemes. We prove that limit solutions satisfy the entropy inequality. In the scalar case, we prove convergence to the unique entropy-satisfying solution if the initial scheme is Total Variation Decreasing (i.e., TVD) and consistent with the entropy condition. Finally, we slightly modify Harten’s high-order schemes such that they obey the previous conditions and thus converge towards the "entropy" solution.

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Article copyright: © Copyright 1988 American Mathematical Society