论文标题
无darcy稳定性的孔隙弹性的准确离散 - 重新审视了Stokes-Biot稳定性
Accurate Discretization Of Poroelasticity Without Darcy Stability -- Stokes-Biot Stability Revisited
论文作者
论文摘要
在此手稿中，我们关注一个问题：Stokes-Biot稳定性的正确概念是什么？由几位作者独立引入了Stokes-Biot稳定的离散化，作为离散Biot的毛弹性方程的一种手段。在消失的存储系数和消失的液压电导率的背景下，此类方案在适当定义的规范方面保留了其稳定性和收敛性。 Stokes-Biot稳定离散化的基本前提是：一部分Stoks稳定性和一个部分混合Darcy稳定性。在本手稿中，我们指出的是，后一种条件可以推广到更广泛的离散空间。特别是：混合Darcy子问题的参数 - 均匀的INF-SUP条件并不是严格必要的，以保留Stokes-Biot稳定稳定的Euler-Galerkin离散化方案当前所享有的实际优势。
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.
