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Volume 21, Issue 4
The Weak Galerkin Finite Element Method for the Dual-Porosity-Stokes Model

Lin Yang, Wei Mu, Hui Peng & Xiuli Wang

DOI: 10.4208/ijnam2024-1023

Int. J. Numer. Anal. Mod., 21 (2024), pp. 587-608.

Published online: 2024-06

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  • Abstract

In this paper, we introduce a weak Galerkin finite element method for the dual-porosity-Stokes model. The dual-porosity-Stokes model couples the dual-porosity equations with the Stokes equations through four interface conditions. In this method, we define several weak Galerkin finite element spaces and weak differential operators. We provide the weak Galerkin scheme for the model, and establish the well-posedness of the numerical scheme. The optimal convergence orders of errors in the energy norm are derived. Finally, we verify the effectiveness of the numerical method with different weak Galerkin elements on different meshes.

  • Keywords

Dual-porosity-Stokes model, weak Galerkin finite element method, discrete weak gradient, discrete weak divergence.

  • AMS Subject Headings

65M60, 65M12, 65M15, 35M10, 35Q35, 76D07, 76S05

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{IJNAM-21-587, author = {Yang , LinMu , WeiPeng , Hui and Wang , Xiuli}, title = {The Weak Galerkin Finite Element Method for the Dual-Porosity-Stokes Model}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2024}, volume = {21}, number = {4}, pages = {587--608}, abstract = {

In this paper, we introduce a weak Galerkin finite element method for the dual-porosity-Stokes model. The dual-porosity-Stokes model couples the dual-porosity equations with the Stokes equations through four interface conditions. In this method, we define several weak Galerkin finite element spaces and weak differential operators. We provide the weak Galerkin scheme for the model, and establish the well-posedness of the numerical scheme. The optimal convergence orders of errors in the energy norm are derived. Finally, we verify the effectiveness of the numerical method with different weak Galerkin elements on different meshes.

}, issn = {2617-8710}, doi = {https://doi.org/10.4208/ijnam2024-1023}, url = {http://global-sci.org/intro/article_detail/ijnam/23203.html} }
TY - JOUR T1 - The Weak Galerkin Finite Element Method for the Dual-Porosity-Stokes Model AU - Yang , Lin AU - Mu , Wei AU - Peng , Hui AU - Wang , Xiuli JO - International Journal of Numerical Analysis and Modeling VL - 4 SP - 587 EP - 608 PY - 2024 DA - 2024/06 SN - 21 DO - http://doi.org/10.4208/ijnam2024-1023 UR - https://global-sci.org/intro/article_detail/ijnam/23203.html KW - Dual-porosity-Stokes model, weak Galerkin finite element method, discrete weak gradient, discrete weak divergence. AB -

In this paper, we introduce a weak Galerkin finite element method for the dual-porosity-Stokes model. The dual-porosity-Stokes model couples the dual-porosity equations with the Stokes equations through four interface conditions. In this method, we define several weak Galerkin finite element spaces and weak differential operators. We provide the weak Galerkin scheme for the model, and establish the well-posedness of the numerical scheme. The optimal convergence orders of errors in the energy norm are derived. Finally, we verify the effectiveness of the numerical method with different weak Galerkin elements on different meshes.

Lin Yang, Wei Mu, Hui Peng & Xiuli Wang. (2024). The Weak Galerkin Finite Element Method for the Dual-Porosity-Stokes Model. International Journal of Numerical Analysis and Modeling. 21 (4). 587-608. doi:10.4208/ijnam2024-1023
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