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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2024 MCQ for Mathematics of Computation is 1.78.

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High-order schemes and entropy condition for nonlinear hyperbolic systems of conservation laws
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by J.-P. Vila PDF
Math. Comp. 50 (1988), 53-73 Request permission

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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Additional Information
  • © Copyright 1988 American Mathematical Society
  • Journal: Math. Comp. 50 (1988), 53-73
  • MSC: Primary 65M10; Secondary 35L65
  • DOI: https://doi.org/10.1090/S0025-5718-1988-0917818-1
  • MathSciNet review: 917818