Comparison of some finite element methods for solving the diffusion-convection-reaction equation

In this paper we describe several finite element methods for solving the diffusion-convection-reaction equation. None of them is new, although the presentation is non-standard in an effort to emphasize the similarities and differences between them. In particular, it is shown that the classical SUPG methods is very similar to an explicit version of the Characteristic-Galerkin method, whereas the Taylor-Galerkin method has a stabilization effect similar to a subgrid scale model, which is in turn related to the introduction of bubble functions.