  We review basic design principles underpinning the construction of mimetic
finite difference and a few finite volume and finite element schemes for mixed
formulations of elliptic problems. For a class of low-order mixed-hybrid
schemes, we show connections between these principles and prove that the
consistency and stability conditions must lead to a member of the mimetic
family of schemes regardless of the selected discretization framework. Finally,
we give two examples of using flexibility of the mimetic framework: derivation
of higher-order schemes and convergent schemes for nonlinear problems with
small diffusion coefficients.
