  A discretization of a continuum theory with constraints or conserved
quantities is called mimetic if it mirrors the conserved laws or constraints of
the continuum theory at the discrete level. Such discretizations have been
found useful in continuum mechanics and in electromagnetism. We have recently
introduced a new technique for discretizing constrained theories. The technique
yields discretizations that are consistent, in the sense that the constraints
and evolution equations can be solved simultaneously, but it cannot be
considered mimetic since it achieves consistency by determining the Lagrange
multipliers. In this paper we would like to show that when applied to general
relativity linearized around a Minkowski background the technique yields a
discretization that is mimetic in the traditional sense of the word. We show
this using the traditional metric variables and also the Ashtekar new
variables, but in the latter case we restrict ourselves to the Euclidean case.
We also argue that there appear to exist conceptual difficulties to the
construction of a mimetic formulation of the full Einstein equations, and
suggest that the new discretization scheme can provide an alternative that is
nevertheless close in spirit to the traditional mimetic formulations.
