  We provide a unified continuum formulation of linearized mechanics, Stokes'
flow and poromechanics in terms of a conservation structure. Starting from this
formulation, we construct corresponding simple and robust finite volume
discretizations for these physical systems, based only on co-located,
cell-centered variables. These discretizations have a minimal discretization
stencil, using only the two neighboring cells to a face to calculate numerical
stresses and fluxes.
  We show well-posedness of a weak statement of the continuous formulation in
appropriate Hilbert spaces, and identify the appropriate weighted norms for the
problem. For the discrete approximations, we prove stability and convergence,
both of which are robust in terms of the material parameters. Numerical
experiments in 3D support the theoretical results, and provide additional
insight into the practical performance of the discretization.
