Volume 10, Issue 3
Mortar Element Method for the Coupling of Navier-Stokes and Darcy Flows

Adv. Appl. Math. Mech., 10 (2018), pp. 710-734.

Published online: 2018-10

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• Abstract

In this paper, we investigate the nonlinear system of Navier-Stokes and Darcy flows coupled by the Beavers-Joseph-Saffman law on the interface. The well-posedness of the weak and numerical solutions are established. Mortar elemen method is introduced to solve the coupled model. Error estimates are derived for the proposed method. We adopt an iterative algorithm to solve the nonlinear scheme generated by the coupled system. Numerical example is provided to verify the theoretical analysis.

• Keywords

Darcy flow, Navier-Stokes equations, finite element method, mortar element.

76D05, 76S05, 65N30

• BibTex
• RIS
• TXT
@Article{AAMM-10-710, author = {Xin Zhao , and Chen , Yanping}, title = {Mortar Element Method for the Coupling of Navier-Stokes and Darcy Flows}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2018}, volume = {10}, number = {3}, pages = {710--734}, abstract = {

In this paper, we investigate the nonlinear system of Navier-Stokes and Darcy flows coupled by the Beavers-Joseph-Saffman law on the interface. The well-posedness of the weak and numerical solutions are established. Mortar elemen method is introduced to solve the coupled model. Error estimates are derived for the proposed method. We adopt an iterative algorithm to solve the nonlinear scheme generated by the coupled system. Numerical example is provided to verify the theoretical analysis.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.OA-2017-0170}, url = {http://global-sci.org/intro/article_detail/aamm/12232.html} }
TY - JOUR T1 - Mortar Element Method for the Coupling of Navier-Stokes and Darcy Flows AU - Xin Zhao , AU - Chen , Yanping JO - Advances in Applied Mathematics and Mechanics VL - 3 SP - 710 EP - 734 PY - 2018 DA - 2018/10 SN - 10 DO - http://doi.org/10.4208/aamm.OA-2017-0170 UR - https://global-sci.org/intro/article_detail/aamm/12232.html KW - Darcy flow, Navier-Stokes equations, finite element method, mortar element. AB -

In this paper, we investigate the nonlinear system of Navier-Stokes and Darcy flows coupled by the Beavers-Joseph-Saffman law on the interface. The well-posedness of the weak and numerical solutions are established. Mortar elemen method is introduced to solve the coupled model. Error estimates are derived for the proposed method. We adopt an iterative algorithm to solve the nonlinear scheme generated by the coupled system. Numerical example is provided to verify the theoretical analysis.

Xin Zhao & Yanping Chen. (2020). Mortar Element Method for the Coupling of Navier-Stokes and Darcy Flows. Advances in Applied Mathematics and Mechanics. 10 (3). 710-734. doi:10.4208/aamm.OA-2017-0170
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