Second-order conservative schemes and the entropy condition

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.