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

Xin Zhao & Yanping Chen

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 wellposedness 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.

  • AMS Subject Headings

76D05, 76S05, 65N30

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{AAMM-10-710, author = {}, 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 wellposedness 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 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 wellposedness 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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