DefinitionDefinition: Literature-sourcedProof: Not applicablePipeline-generatedjudge pass (gpt-6-luna)

How statement and proof provenance work

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Tadmor entropy-conservative two-point flux

Definition

Let $(η, q)$ be a convex entropy pair on an open domain $A$ , with entropy variable $v$ and potential $ψ$ as in Convex entropy pairs, entropy variables, and entropy potentials for systems. A continuous two-point flux $F^{e c} : A \times A \to R^{m}$ is entropy-conservative in Tadmor's sense if it is consistent and symmetric, $F^{e c} (U, U) = F (U)$ , and satisfies the exact jump identity $(v (U_{R}) - v (U_{L}))^{T} F^{e c} (U_{L}, U_{R}) = ψ (U_{R}) - ψ (U_{L})$ for every pair $U_{L}, U_{R} \in A$ . This definition asserts no existence for a prescribed entropy pair.

Depends on

Convex entropy pairs, entropy variables, and entropy potentials for systems

Used by

Dependency tree · two levels

2 results within two dependency steps of this one, each drawn at its shortest distance from it. An arrow runs from a result to what uses it, so the chart reads left to right and ends at this result, which carries a heavier outline. Every node is a link to that result. Click elsewhere on the chart to enlarge it.

Sources

E. Tadmor, Entropy Stable Schemes for Hyperbolic Conservation Laws, Handbook of Numerical Methods for Hyperbolic Problems, Vol. 17 (standard reference, not scraped)
R. Bürger, P. E. Méndez, and C. Parés, On Entropy Stable Schemes for Degenerate Parabolic Multispecies Kinematic Flow Models (standard reference, not scraped)