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

作     者：Mardal, Kent-Andre Rognes, Marie E. Thompson, Travis B. 

作者机构：Univ Oslo Dept Math Oslo Norway Simula Res Lab Fornebu Norway Simula Res Lab Dept Sci Comp & Numer Anal Fornebu Norway Univ Oxford Math Inst Oxford England 

出 版 物：《BIT NUMERICAL MATHEMATICS》 (BIT数值数学)

年 卷 期：2021年第61卷第3期

页      面：941-976页

核心收录：

学科分类：12[管理学] 1201[管理学-管理科学与工程(可授管理学、工学学位)] 07[理学] 070105[理学-运筹学与控制论] 0835[工学-软件工程] 0701[理学-数学] 

基　　金：Research Council of Norway Research Council of Norway under the FRINATEK Young Research Talents Programme [250731/F20] EPSRC [EP/R020205/1] Funding Source: UKRI 

主　　题：Poroelasticity Biot’ s equations Mixed method Darcy stability Stokes– Biot stability 

摘      要：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.