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["B. Emek Abali" <question158693@xxxxxxxxxxxxxxxxxxxxx>]

Question #158693 on DOLFIN changed:
https://answers.launchpad.net/dolfin/+question/158693

B. Emek Abali proposed the following answer:
as fas as I know the "conservative"ness of the FVM is the divergence
free solution. In fluid dynamics the solution is the velocity field and
from the balance of mass (under the assumption of constant in time and
constant in space mass density) divergence of velocities is zero can be
found. This (widely known as incompressibility) condition is added into
variational formulation in fem and already implemented into the fvm (as
constant volume). Therefore any element type in fem with constant
velocity (constant form functions) is the fvm formulation (at least to
me as an engineer :)

But do not forget two assumptions in the formulations, one is the Gauss
theorem is used, so risky but we assumed the continuity of the solution.
Against that ALSO the evaluation on the boundaries (of each element) are
popular (discontinuous galerkin) and FEniCS perfectly allow all these
studies. Another tiny (but actually a big headache) assumption is the
mass density is constant in time assumption. This is done also in
somehow other ways in fem (in the formulation) in fvm (not even
mentioned).

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