  We are interested in the discretisation of the steady version of hyperbolic
problems. We first show that all the known schemes (up to our knowledge) can be
rephrased in a common framework. Using this framework, we first show all the
known schemes have a flux formulation, with an explicit construction of the
flux, and thus are locally conservative. This is well known for the finite
volume schemes or the discontinuous Galerkin ones, much less known for the
continuous finite element methods. We also show that Tadmor's entropy stability
formulation can naturally be rephrased in this framework as an additional
conservation relation discretisation, and using this, we show some conenction
with the recent papers [1, 2, 3, 4]. This contribution is an enhanced version
of [5].
