The authors introduce a new stabilization method in order to integrate a one dimensional convection-diffusion-reaction boundary value problem. The method works without any a priori knowledge of the physics of the flow and is essentially based on the augmented space idea. The classical finite element space is enlarged with the so-called space of bubbles. The authors provide all details about the choice of location of the nodes in this space corresponding to diffusion-dominated, convection-dominated as well as reaction-dominated regimes. The transition from one regim to another is continuous. Some numerical experiments carried out on test problems underline the robustness of the method.