On a convection-diffusion problem with a weak layer

In this article we consider a model linear convection-diffusion problem with a weak layer. We analyze the singular-perturbation nature of the problem and show that no special precautions are required to cope with the weak layer: a standard upwind scheme on a (quasi-)uniform mesh is sufficient. We give a simple analysis for the method. Thus highlighting that not all problems with a small parameter multiplying the highest-order derivative are suitable for studying boundary-layer phenomena.