  This paper contains construction and analysis a finite element approximation
for convection dominated diffusion problems with full coefficient matrix on
general simplicial partitions in $R^d$, $d=2,3$. This construction is quite
close to the scheme of Xu and Zikatanov (Math. Comp. 1999) where a diagonal
coefficient matrix has been considered. The scheme is of the class of
exponentially fitted methods that does not use upwind or checking the flow
direction. It is stable for sufficiently small discretization step-size
assuming that the boundary value problem for the convection-diffusion equation
is uniquely solvable. Further, it is shown that, under certain conditions on
the mesh the scheme is monotone. Convergence of first order is derived under
minimal smoothness of the solution.
