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Mathematics of Computation

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



Second-order conservative schemes and the entropy condition

Author: Maria E. Schonbek
Journal: Math. Comp. 44 (1985), 31-38
MSC: Primary 65M10; Secondary 35L65
MathSciNet review: 771028
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Abstract: We consider numerical approximations to solutions of systems of hyperbolic conservation laws of the form $\partial u/\partial t + \partial f(u)/\partial x = 0$, $u \in {{\mathbf {R}}^n}$ and $f:{R^n} \to {R^n}$ smooth. We show that conservative three-point second-order accurate methods cannot satisfy a local entropy inequality.

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Article copyright: © Copyright 1985 American Mathematical Society