Stability of an upwind Petrov Galerkin discretization of convection   diffusion equations
  We study a numerical method for convection diffusion equations, in the regime of small viscosity. It can be described as an exponentially fitted conforming Petrov-Galerkin method. We identify norms for which we have both continuity and an inf-sup condition, which are uniform in mesh-width and viscosity, up to a logarithm, as long as the viscosity is smaller than the mesh-width or the crosswind diffusion is smaller than the streamline diffusion. The analysis allows for the formation of a boundary layer. 
Snorre H. Christiansen, Tore G. Halvorsen, Torquil M. S{\o}rensen
math.NA