  This paper is devoted to the construction and analysis of the finite element
approximations for the $H(D)$ convection-diffusion problems, where $D$ can be
chosen as ${\rm grad}$, ${\rm curl}$ or ${\rm div}$ in 3D case. An essential
feature of these constructions is to properly average the PDE coefficients on
the sub-simplexes. The schemes are of the class of exponential fitting methods
that result in special upwind schemes when the diffusion coefficient approaches
to zero. Their well-posedness are established for sufficiently small mesh size
assuming that the convection-diffusion problems are uniquely solvable.
Convergence of first order is derived under minimal smoothness of the solution.
Some numerical examples are given to demonstrate the robustness and
effectiveness for general convection-diffusion problems.
