  Since the celebrated theorem of Lax and Wendroff, we know a necessary
condition that any numerical scheme for hyperbolic problem should satisfy: it
should be written in flux form. A variant can also be formulated for the
entropy. Even though some schemes, as for example those using continuous finite
element, do not formally cast into this framework, it is a very convenient one.
In this paper, we revisit this, introduce a different notion of local
conservation which contains the previous one in one space dimension, and
explore its consequences. This gives a more flexible framework that allows to
get, systematically, entropy stable schemes, entropy dissipative ones, or
accomodate more constraints. In particular, we can show that continuous finite
element method can be rewritten in the finite volume framework, and all the
quantities involved are explicitly computable. We end by presenting the only
counter example we are aware of, i.e a scheme that seems not to be rewritten as
a finite volume scheme.
