一种具有二阶收敛性的Stokes-Darcy耦合问题的统一混合有限元近似
A Unified Mixed Finite Element Approximation for Stokes-Darcy Coupling Problems with Second-Order Convergence
摘要: 文章给出了平面区域中Stokes-Darcy耦合问题的具有二阶收敛精度的统一近似格式。在这项工作中，我们修改了Darcy变分格式并增强了其正定性，使我们能够将P2元改进的Mini元应用于整个Stokes-Darcy耦合问题。此外，由于这种二阶格式在耦合界面上有足够的自由度，因此不需要在界面上添加额外的函数来稳定离散问题。最后，通过两个算例验证了理论分析，证明了该格式对于具有不同形状的耦合界面的问题具有良好的稳定性和准确性。
Abstract: In this paper, a unified approximation with second-order convergence accuracy for the Stokes-Darcy coupled problem in the plane domain is presented. In this work, we modify the Darcy problem and enhance its positive definiteness, which allows us to apply the Mini-element improved with P2-element to the entire coupled Stokes-Darcy problem. Moreover, since this second-order format has sufficient degrees of freedom on the coupled interface, we do not need to add additional functions on the interface to stabilize the discrete problem. Finally, the theoretical analysis is verified by two arithmetic examples, which prove that the scheme has good stability and accuracy for problems with different shapes of coupled interfaces.
文章引用：谢富伟, 马晓华. 一种具有二阶收敛性的Stokes-Darcy耦合问题的统一混合有限元近似[J]. 应用数学进展, 2025, 14(2): 388-398. https://doi.org/10.12677/aam.2025.142079

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