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 - <p style="text-align: justify;">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.</p>