标题： 分析与消除耦合Stokes-Darcy问题中的数值压力依赖性 显示英文标题

标题： Analysis and Elimination of Numerical Pressure Dependency in Coupled Stokes-Darcy Problem

摘要： 本文提出了一种针对耦合Stokes-Darcy系统的压力稳健的混合有限元方法（FEM）。我们重新审视了Layton等人[2002]的严格理论框架，在该框架中速度和压力误差相互耦合，掩盖了压力对速度精度的影响。为了研究压力依赖性，我们引入了一个辅助的速度投影，它保留了离散散度和界面连续性约束。通过分析离散速度与投影速度之间的差异，我们严格证明了经典FEM由于不精确的散度强制和近似界面条件而导致了压力相关的相容性误差。为消除这些误差，我们设计了一种使用无散度重构算子的压力稳健方法，该方法强制执行精确的散度约束和界面连续性。数值例子验证了这一理论：在高压或低粘度情况下，所提出的方法相比经典方法将速度误差减少了几个数量级。 显示英文摘要

摘要： This paper presents a pressure-robust mixed finite element method (FEM) for the coupled Stokes-Darcy system. We revisits the rigorous theoretical framework of Layton et al. [2002], where velocity and pressure errors are coupled, masking pressure's influence on velocity accuracy. To investigate the pressure dependency, we introduce a auxiliary velocity projection that preserves discrete divergence and interface continuity constraints. By analyzing the difference between the discrete and projected velocities, we rigorously prove that classical FEM incurs pressure-dependent consistency errors due to inexact divergence enforcement and approximate interface conditions. To eliminate these errors, we design a pressure-robust method using divergence-free reconstruction operator, which enforce exact divergence constraint and interface continuity. Numerical examples confirm the theory: under high-pressure or low-viscosity, the proposed method reduces velocity errors by orders of magnitude compared to classical method.