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Volume 21, Issue 4
A Stabilizer-Free Weak Galerkin Finite Element Method for the Darcy-Stokes Equations

Kai He, Junjie Chen, Li Zhang & Maohua Ran

DOI: 10.4208/ijnam2024-1018

Int. J. Numer. Anal. Mod., 21 (2024), pp. 459-475.

Published online: 2024-06

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  • Abstract

In this paper, we propose a new method for the Darcy-Stokes equations based on the stabilizer-free weak Galerkin finite element method. In the proposed method, we remove the stabilizer term by increasing the degree of polynomial approximation space of the weak gradient operator. Compared with the classical weak Galerkin finite element method, it will not increase the size of global stiffness matrix. We show that the new algorithm not only has a simpler formula, but also reduces the computational complexity. Optimal order error estimates are established for the corresponding numerical approximation in various norms. Finally, we numerically illustrate the accuracy and convergence of this method.

  • Keywords

Stabilizer-free, weak Galerkin finite element method, Darcy-Stokes equations, weak gradient operator, optimal order error estimates.

  • AMS Subject Headings

65N12, 65N30

  • Copyright

COPYRIGHT: © Global Science Press

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  • TXT
@Article{IJNAM-21-459, author = {He , KaiChen , JunjieZhang , Li and Ran , Maohua}, title = {A Stabilizer-Free Weak Galerkin Finite Element Method for the Darcy-Stokes Equations}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2024}, volume = {21}, number = {4}, pages = {459--475}, abstract = {

In this paper, we propose a new method for the Darcy-Stokes equations based on the stabilizer-free weak Galerkin finite element method. In the proposed method, we remove the stabilizer term by increasing the degree of polynomial approximation space of the weak gradient operator. Compared with the classical weak Galerkin finite element method, it will not increase the size of global stiffness matrix. We show that the new algorithm not only has a simpler formula, but also reduces the computational complexity. Optimal order error estimates are established for the corresponding numerical approximation in various norms. Finally, we numerically illustrate the accuracy and convergence of this method.

}, issn = {2617-8710}, doi = {https://doi.org/10.4208/ijnam2024-1018}, url = {http://global-sci.org/intro/article_detail/ijnam/23198.html} }
TY - JOUR T1 - A Stabilizer-Free Weak Galerkin Finite Element Method for the Darcy-Stokes Equations AU - He , Kai AU - Chen , Junjie AU - Zhang , Li AU - Ran , Maohua JO - International Journal of Numerical Analysis and Modeling VL - 4 SP - 459 EP - 475 PY - 2024 DA - 2024/06 SN - 21 DO - http://doi.org/10.4208/ijnam2024-1018 UR - https://global-sci.org/intro/article_detail/ijnam/23198.html KW - Stabilizer-free, weak Galerkin finite element method, Darcy-Stokes equations, weak gradient operator, optimal order error estimates. AB -

In this paper, we propose a new method for the Darcy-Stokes equations based on the stabilizer-free weak Galerkin finite element method. In the proposed method, we remove the stabilizer term by increasing the degree of polynomial approximation space of the weak gradient operator. Compared with the classical weak Galerkin finite element method, it will not increase the size of global stiffness matrix. We show that the new algorithm not only has a simpler formula, but also reduces the computational complexity. Optimal order error estimates are established for the corresponding numerical approximation in various norms. Finally, we numerically illustrate the accuracy and convergence of this method.

Kai He, Junjie Chen, Li Zhang & Maohua Ran. (2024). A Stabilizer-Free Weak Galerkin Finite Element Method for the Darcy-Stokes Equations. International Journal of Numerical Analysis and Modeling. 21 (4). 459-475. doi:10.4208/ijnam2024-1018
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