  This contribution summarizes the recent work carried out to analyze the
behavior of the hyperbolic sector of the Fully Constrained Formulation (FCF)
derived in Bonazzola et al. 2004. The numerical experiments presented here
allows one to be confident in the performances of the upgraded version of
CoCoNuT's code by replacing the Conformally Flat Condition (CFC) approximation
of the Einstein equations by the FCF.
