Accurate discretization of poroelasticity without Darcy stability --- Stokes-Biot stability revisited

In this manuscript we focus on the question: what is the correct notion of Stokes-Biot stability?
Stokes-Biot stable discretizations have been introduced, independently by several authors, as a means of
discretizing Biot’s equations of poroelasticity; such schemes retain their stability and convergence properties, with respect to appropriately defined norms, in the context of a vanishing storage coefficient and
a vanishing hydraulic conductivity. The basic premise of a Stokes-Biot stable discretization is: one part
Stokes stability and one part mixed Darcy stability. In this manuscript we remark on the observation that
the latter condition can be generalized to a wider class of discrete spaces. In particular: a parameter-uniform
inf-sup condition for a mixed Darcy sub-problem is not strictly necessary to retain the practical advantages
currently enjoyed by the class of Stokes-Biot stable Euler-Galerkin discretization schemes.