Whether the flux-derivative damping term can be omitted

Determine whether the flux-derivative contribution in the damping coefficient of Scheme D can be set to zero while retaining convergence to the correct entropy solution for non-convex conservation laws.

Background

The practical damping coefficient $D_j$ contains an interior flux-derivative term weighted by $\epsilon_1$ and an interface-jump term weighted by $\epsilon_2$. The flux-derivative term is analytically important in the paper's entropy and compensated-compactness arguments, but numerical experiments suggest that it may sometimes be unnecessary, especially for certain systems and multidimensional tests.

For non-convex scalar examples, however, setting $\epsilon_1=0$ can produce incorrect solutions when the interface damping is moderate. The paper therefore leaves unresolved the general conditions under which the flux-derivative term may be omitted.