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A steady convection-diffusion problem is defined by the following equations:
The main difficulty of these problems is that Galerkin formulation
provides poor results when convective terms are important. In
fact, spurious oscillations appear when Péclet number
( )
is greater than one. Therefore, in order to avoid excessive
mesh refinement, it is necessary to use more adequate (stabilized)
formulations such as Streamline-Upwind (SU), Streamline-Upwind
Petrov Galerkin (SUPG), Galerkin Least-Squares (GLS) or Subgrid
Scales (SGS).
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One-dimensional convection-diffusion problem 
Two-dimensional convection-diffusion problem
Two-dimensional convection-diffusion-reaction problem
Introduction