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Volume 43, Issue 4
A Weak Galerkin Mixed Finite Element Method for linear Elasticity Without Enforced Symmetry

Yue Wang & Fuzheng Gao

DOI: 10.4208/jcm.2404-m2023-0250

J. Comp. Math., 43 (2025), pp. 898-917.

Published online: 2025-07

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  • Abstract

A weak Galerkin mixed finite element method is studied for linear elasticity problems without the requirement of symmetry. The key of numerical methods in mixed formulation is the symmetric constraint of numerical stress. In this paper, we introduce the discrete symmetric weak divergence to ensure the symmetry of numerical stress. The corresponding stabilizer is presented to guarantee the weak continuity. This method does not need extra unknowns. The optimal error estimates in discrete $H^1$ and $L^2$ norms are established. The numerical examples in 2D and 3D are presented to demonstrate the efficiency and locking-free property.

  • Keywords

Linear elasticity, Discrete symmetric weak divergence, Mixed finite element method, Weak Galerkin finite element method.

  • AMS Subject Headings

65M60, 74B10, 74S05

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JCM-43-898, author = {Wang , Yue and Gao , Fuzheng}, title = {A Weak Galerkin Mixed Finite Element Method for linear Elasticity Without Enforced Symmetry}, journal = {Journal of Computational Mathematics}, year = {2025}, volume = {43}, number = {4}, pages = {898--917}, abstract = {

A weak Galerkin mixed finite element method is studied for linear elasticity problems without the requirement of symmetry. The key of numerical methods in mixed formulation is the symmetric constraint of numerical stress. In this paper, we introduce the discrete symmetric weak divergence to ensure the symmetry of numerical stress. The corresponding stabilizer is presented to guarantee the weak continuity. This method does not need extra unknowns. The optimal error estimates in discrete $H^1$ and $L^2$ norms are established. The numerical examples in 2D and 3D are presented to demonstrate the efficiency and locking-free property.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.2404-m2023-0250}, url = {http://global-sci.org/intro/article_detail/jcm/24265.html} }
TY - JOUR T1 - A Weak Galerkin Mixed Finite Element Method for linear Elasticity Without Enforced Symmetry AU - Wang , Yue AU - Gao , Fuzheng JO - Journal of Computational Mathematics VL - 4 SP - 898 EP - 917 PY - 2025 DA - 2025/07 SN - 43 DO - http://doi.org/10.4208/jcm.2404-m2023-0250 UR - https://global-sci.org/intro/article_detail/jcm/24265.html KW - Linear elasticity, Discrete symmetric weak divergence, Mixed finite element method, Weak Galerkin finite element method. AB -

A weak Galerkin mixed finite element method is studied for linear elasticity problems without the requirement of symmetry. The key of numerical methods in mixed formulation is the symmetric constraint of numerical stress. In this paper, we introduce the discrete symmetric weak divergence to ensure the symmetry of numerical stress. The corresponding stabilizer is presented to guarantee the weak continuity. This method does not need extra unknowns. The optimal error estimates in discrete $H^1$ and $L^2$ norms are established. The numerical examples in 2D and 3D are presented to demonstrate the efficiency and locking-free property.

Wang , Yue and Gao , Fuzheng. (2025). A Weak Galerkin Mixed Finite Element Method for linear Elasticity Without Enforced Symmetry. Journal of Computational Mathematics. 43 (4). 898-917. doi:10.4208/jcm.2404-m2023-0250
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