Extension of the complete flux scheme to time-dependent conservation laws

We present the stationary and transient complete flux schemes for the advection-diffusion-reaction equation. In the first scheme, the numerical flux is derived from a local BVP for the stationary equation. The transient scheme is an extension, since it includes the time derivative in the flux computation. The resulting semidiscretization is an implicit ODE system, which has much smaller dissipation and dispersion errors than the semidiscretization based on the stationary flux, at least for smooth problems. Both schemes are validated for a test problem