  The paper is devoted to the spectral analysis of effective preconditioners
for linear systems obtained via a Finite Element approximation to
diffusion-dominated convection-diffusion equations. We consider a model setting
in which the structured finite element partition is made by equi-lateral
triangles. Under such assumptions, if the problem is coercive, and the
diffusive and convective coefficients are regular enough, then the proposed
preconditioned matrix sequences exhibit a strong clustering at unity, the
preconditioning matrix sequence and the original matrix sequence are spectrally
equivalent, and the eigenvector matrices have a mild conditioning. The obtained
results allow to show the optimality of the related preconditioned Krylov
methods. %It is important to stress that The interest of such a study relies on
the observation that automatic grid generators tend to construct equi-lateral
triangles when the mesh is fine enough. Numerical tests, both on the model
setting and in the non-structured case, show the effectiveness of the proposal
and the correctness of the theoretical findings.
