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.

在此手稿中，我们重点关注的问题是：斯托克斯-比奥稳定性的正确概念是什么？Stokes–Biot稳定离散化已被多位作者独立引入，以离散化Biot的孔隙弹性方程。相对于适当定义的规范，这种方案在存储系数消失和水力传导率消失的情况下仍保持其稳定性和收敛性。Stokes-Biot稳定离散的基本前提是：一部分是Stokes稳定性，另一部分是混合Darcy稳定性。在本手稿中，我们评论说后一种情况可以推广到更广泛的离散空间类别。尤其是：