NITSCHE'S TYPE STABILIZATION FOR THE FULLY MIXED NAVIER-STOKES/DARCY PROBLEM

Jiaping Yu; Yuhong Zhang

doi:10.11948/20200249

2021 Volume 11 Issue 3

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Jiaping Yu, Yuhong Zhang. NITSCHE'S TYPE STABILIZATION FOR THE FULLY MIXED NAVIER-STOKES/DARCY PROBLEM[J]. Journal of Applied Analysis & Computation, 2021, 11(3): 1481-1493. doi: 10.11948/20200249

Citation:

Jiaping Yu, Yuhong Zhang. NITSCHE'S TYPE STABILIZATION FOR THE FULLY MIXED NAVIER-STOKES/DARCY PROBLEM[J]. Journal of Applied Analysis & Computation, 2021, 11(3): 1481-1493. doi: 10.11948/20200249

NITSCHE'S TYPE STABILIZATION FOR THE FULLY MIXED NAVIER-STOKES/DARCY PROBLEM

Jiaping Yu¹,
Yuhong Zhang^2, ,

1.
College of Science, Institute for Nonlinear Sciences, Donghua University, Shanghai, 201620, China
2.
College of Mathematics and Computer Science, Hunan Normal University, Changsha, Hunan, 410081, China

Corresponding author: Email: yhzhang@hunnu.edu.cn(Y. H. Zhang)
Fund Project: The authors were supported partially supported by NSFC (Grant No. 11801170, 11501097) and Fundamental Research Funds for the Central Universities 2232019D3-39

Abstract

Abstract

In this paper, we present and analyze a fully mixed finite element scheme for the Navier-Stokes/Darcy problem based on the Nitsche's type interface stabilizations, in the fluid region coupled with the porous media domain. The reasonable parameter $ \delta>0 $, which is independent of mesh size $ h $, will guarantee the stability and optimal convergence of our stabilized scheme. Moreover, we explicitly derive the dependence and requirement of the stabilization parameter $ \delta $ for the optimal error estimates, while the numerical tests support the stability and efficiency of this stabilized mixed method.
- Navier-Stokes/Darcy problem /
- mixed finite elements /
- Nitsche's method /
- Beavers-Joseph-Saffman
MSC: 65M12, 65M60

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References

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