Before revision:  It is shown that the average of the solutions reconstructed at a face by Van Leer's kappa-scheme recovers a cubic solution exactly with kappa = 1/3, the same is true for the average of the nonlinear fluxes evaluated by the reconstructed solutions, and a dissipation term does not contribute to the leading third-order  error.
After revision:  It is shown that the average of the solutions reconstructed at a face by Van Leer's kappa-scheme recovers a cubic solution exactly with kappa = 1/3, the same is true for the average of the nonlinear fluxes evaluated by the reconstructed solutions, and a dissipation term is already sufficiently small with a third-order error.