涡量形式下Biot–Brinkman方程的鲁棒有限元方法与求解器
Robust finite element methods and solvers for the Biot--Brinkman equations in vorticity form
AI总结：
本文针对可变形多孔介质粘性流稳态耦合的Biot–Brinkman方程涡量形式，提出基于参数加权空间的散度相容有限元方法，证明其可解性与参数鲁棒最优误差估计，通过数值算例验证了方法及块对角预处理器的有效性。
摘要：
本文针对可变形多孔介质中粘性流动的稳态耦合问题，采用散度相容的渗流通量，提出了一种新的公式体系及适配的有限元方法。该方法基于参数加权空间，可对连续问题与离散问题开展更精确、更具鲁棒性的分析。此外，我们对所提方法进行了可解性分析，并在合适的范数下推导得到最优误差估计；结果表明，当Lamé参数较大、渗透率与储水系数较小时，这些误差估计仍具备鲁棒性。为验证方法的有效性，我们提供了若干代表性数值算例，包括收敛性验证、孔隙弹性通道流模拟，并测试了块对角预处理器关于模型参数的鲁棒性。
英文摘要：
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 Lamé 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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
