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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DOI:
https://doi.org/10.1090/S0025-5718-1988-0917818-1

Article copyright:
© Copyright 1988
American Mathematical Society