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 corresponding stationary equation. The transient scheme is an extension, since it includes the time derivative in the flux computation. The resulting semidiscretisation is an implicit ODE system, which has much smaller dissipation and dispersion errors than the semidiscretisation based on the stationary flux, at least for smooth problems. Both schemes are validated for a test problem.