In this paper, we propose a multiphysics mixed finite element method with Nitsche's technique for Stokes-poroelasticity problem. Firstly, we present a multiphysics reformulation of poroelasticity part of the original problem by introducing two pseudo-pressures to reveal the underlying deformation and diffusion multi physical processes in the Stokes-poroelasticity problem. Then, we prove the existence and uniqueness of weak solution of the reformulated and original problem. And we use Nitsche's technique to approximate the coupling condition at the interface to propose a loosely-coupled time-stepping method -- multiphysics mixed finite element method for space variables, and we decouple the reformulated problem into three sub-problems at each time step -- a Stokes problem, a generalized Stokes problem and a mixed diffusion problem. Also, we give the stability analysis and error estimates of the loosely-coupled time-stepping method.
翻译:在本文中,我们提出一种多物理混合限量元素方法,与尼采技术结合,解决斯托克斯-多动弹性问题。首先,我们提出对最初问题的孔径性部分进行多物理重新配制,采用两种假压力,以揭示斯托克斯-多动性问题中潜在的变形和扩散多物理过程。然后,我们证明重塑和原始问题的薄弱解决办法的存在和独特性。我们用尼采技术来比较接口的混合条件,以提出一种松散的混合时间步态方法 -- -- 空间变量的多物理混合定点元素方法,我们将重新组合的问题分化为每个步骤的三个子问题 -- -- 一个斯托克斯问题,一个普遍化的斯托克斯问题和一个混合扩散问题。此外,我们给出了松散时间步法的稳定性分析和误差估计。