Second-Order Conservative Schemes and the Entropy Condition
Copyright policy )Second-Order Conservative Schemes and the Entropy Condition
We consider numerical approximations to solutions of systems of hyperbolic conservation laws of the form ∂ u / ∂ t + ∂ f ( u ) / ∂ x = 0 \partial u/\partial t + \partial f(u)/\partial x = 0 , u ∈ R n u \in {{\mathbf {R}}^n} and f : R n → R n f:{R^n} \to {R^n} smooth. We show that conservative three-point second-order accurate methods cannot satisfy a local entropy inequality.
Hyperbolic conservation laws, entropy dissipation condition, discrete entropy inequality, systems, three-point second-order methods, conservative method, Stability and convergence of numerical methods for boundary value problems involving PDEs
Hyperbolic conservation laws, entropy dissipation condition, discrete entropy inequality, systems, three-point second-order methods, conservative method, Stability and convergence of numerical methods for boundary value problems involving PDEs
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