In this paper, we propose a new formulation and a suitable finite element method for the steady coupling of viscous flow in deformable porous media using divergence-conforming filtration fluxes. The proposed method is based on the use of parameter-weighted spaces, which allows for a more accurate and robust analysis of the continuous and discrete problems. Furthermore, we conduct a solvability analysis of the proposed method and derive optimal error estimates in appropriate norms. These error estimates are shown to be robust in the case of large Lam\'e parameters and small permeability and storativity coefficients. To illustrate the effectiveness of the proposed method, we provide a few representative numerical examples, including convergence verification, poroelastic channel flow simulation, and test the robustness of block-diagonal preconditioners with respect to model parameters.

翻译：本文针对可变形多孔介质中黏性流动的稳态耦合问题，提出了一种基于散度相容过滤通量的新变分形式与相应的有限元方法。该方法采用参数加权空间，能够对连续问题与离散问题进行更精确鲁棒的数值分析。进一步地，我们进行了所提方法的可解性分析，并在适当范数下推导了最优误差估计。这些误差估计在Lame参数较大、渗透率与储集系数较小的情形下展现出鲁棒性。为验证方法有效性，我们提供了若干代表性数值算例，包括收敛性验证、多孔弹性通道流动模拟，以及测试块对角预条件子对模型参数的鲁棒性。