Title: Equivalence between Mimetic Finite Difference, Hybrid Finite Volume
and Mixed Finite Volume methods

Abstract: The Mimetic Finite Difference, Hybrid Finite Volume and Mixed Finite
Volume are numerical methods to approximate diffusion equation, and have
been recently developed in a quite separate way. Each of this method is based
on different but natural principles, which can be roughly stated as:
constructing discrete operators which mimicks the duality properties of
continuous operators (Mimetic Finite Difference), constructing a consistent discrete gradient
and using it to build a discrete variational formulation (Hybrid Finite Volume),
using the fluxes as primal unknowns to write the physical laws
- balance, conservativity - and link them via a penalized Taylor expansion to
the cell unknowns (Mixed Finite Volume).

In this talk, we show that, modulo some minor modification/generalizations,
these three schemes are in fact identical. As a consequence of this equivalence,
the tools and results applying to one of these methods also apply to the others,
and some new insights can be gained on each scheme.