Fluid models have successfully explained the physics of a variety of plasmas. To solve the fluid model, the discretization scheme commonly used is the exponential difference scheme (EDS) (Sharfetter D et al 1969 IEEE Trans. Electron Devices 16 64–77). We present an extension of the EDS, the complete flux scheme (ten Thije Boonkkamp J H M et al 2011 J. Sci. Comput. 46 47–70) and show that for typical glow discharge models it is ten times more accurate. The Péclet number is the key parameter throughout the paper. A new interpretation of this number is presented. It is then used to explain the glow discharge structure and to formulate a necessary condition for the validity of the local field approximation.