Numerical analysis for the mixed Navier–Stokes and Darcy Problem with the Beavers–Joseph interface condition
Numerical analysis for the mixed Navier–Stokes and Darcy Problem with the Beavers–Joseph interface condition
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DOI：
10.1002/num.21933
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发表时间：
2015-07
影响因子：
3.9
通讯作者：
Liyun Zuo;Yanren Hou
中科院分区：
文献类型：
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作者：
Liyun Zuo;Yanren Hou
本文考虑了具有Beavers-Joseph界面条件的Navier-Stokes和Darcy耦合问题。在适当的物理参数α和ν的限制下，证明了弱解的存在性和局部唯一性.然后，我们提出了一个耦合的有限元格式和一个解耦和线性化的格式基于两个网格的有限元。在适当的约束条件下，得到了它们的最优误差估计。最后通过数值实验验证了理论结果的正确性以及解耦线性化两重网格算法的有效性。© 2014 Wiley Periodicals，Inc. Numer Methods Partial Differential Eq 31：1009-1030，2015
In this article, we consider the coupled Navier–Stokes and Darcy problem with the Beavers–Joseph interface condition. With suitable restrictions of physical parameters α and ν, we prove the existence and local uniqueness of a weak solution. Then we propose a coupled finite element scheme and a decoupled and linearized scheme based on two‐grid finite element. Under suitable further restrictions, their optimal error estimates are obtained. Finally numerical experiments indicate the validity of the theoretical results as well as the efficiency and effectiveness of the decoupled and linearized two‐grid algorithm. © 2014 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 31: 1009–1030, 2015