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Volume 15, Issue 1
A Weak Galerkin Method for the Coupled Darcy-Stokes Problem with a Nonstandard Transmission Condition on the Stokes Boundary

Jingjun Zhao, Zhiqiang Lv & Yang Xu

DOI: 10.4208/eajam.2023-034.260923

East Asian J. Appl. Math., 15 (2025), pp. 29-52.

Published online: 2025-01

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  • Abstract

In this paper, we study a coupled problem of Darcy’s law and Stokes equation with nonlinear slip boundary conditions. We derive a variational inequality for the coupled problem in detail. Then we introduce and analyze a weak Galerkin method to solve the coupled problem numerically. Under proper regularity assumptions, we obtain the optimal error estimate $\mathscr{O}(h)$ in newly defined $h$-norms. Finally, we give some numerical results to support the theoretical conclusions.

  • Keywords

Coupled Darcy-Stokes problem, variational inequality, weak Galerkin method, error estimate.

  • AMS Subject Headings

65N15, 65N30

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{EAJAM-15-29, author = {Zhao , JingjunLv , Zhiqiang and Xu , Yang}, title = {A Weak Galerkin Method for the Coupled Darcy-Stokes Problem with a Nonstandard Transmission Condition on the Stokes Boundary}, journal = {East Asian Journal on Applied Mathematics}, year = {2025}, volume = {15}, number = {1}, pages = {29--52}, abstract = {

In this paper, we study a coupled problem of Darcy’s law and Stokes equation with nonlinear slip boundary conditions. We derive a variational inequality for the coupled problem in detail. Then we introduce and analyze a weak Galerkin method to solve the coupled problem numerically. Under proper regularity assumptions, we obtain the optimal error estimate $\mathscr{O}(h)$ in newly defined $h$-norms. Finally, we give some numerical results to support the theoretical conclusions.

}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.2023-034.260923 }, url = {http://global-sci.org/intro/article_detail/eajam/23740.html} }
TY - JOUR T1 - A Weak Galerkin Method for the Coupled Darcy-Stokes Problem with a Nonstandard Transmission Condition on the Stokes Boundary AU - Zhao , Jingjun AU - Lv , Zhiqiang AU - Xu , Yang JO - East Asian Journal on Applied Mathematics VL - 1 SP - 29 EP - 52 PY - 2025 DA - 2025/01 SN - 15 DO - http://doi.org/10.4208/eajam.2023-034.260923 UR - https://global-sci.org/intro/article_detail/eajam/23740.html KW - Coupled Darcy-Stokes problem, variational inequality, weak Galerkin method, error estimate. AB -

In this paper, we study a coupled problem of Darcy’s law and Stokes equation with nonlinear slip boundary conditions. We derive a variational inequality for the coupled problem in detail. Then we introduce and analyze a weak Galerkin method to solve the coupled problem numerically. Under proper regularity assumptions, we obtain the optimal error estimate $\mathscr{O}(h)$ in newly defined $h$-norms. Finally, we give some numerical results to support the theoretical conclusions.

Zhao , JingjunLv , Zhiqiang and Xu , Yang. (2025). A Weak Galerkin Method for the Coupled Darcy-Stokes Problem with a Nonstandard Transmission Condition on the Stokes Boundary. East Asian Journal on Applied Mathematics. 15 (1). 29-52. doi:10.4208/eajam.2023-034.260923
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