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A Weak Galerkin Mixed Finite Element Method for linear Elasticity Without Enforced Symmetry

A Weak Galerkin Mixed Finite Element Method for linear Elasticity Without Enforced Symmetry

Year:    2025

Author:    Yue Wang, Fuzheng Gao

Journal of Computational Mathematics, Vol. 43 (2025), Iss. 4 : pp. 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 H1 and L2 norms are established. The numerical examples in 2D and 3D are presented to demonstrate the efficiency and locking-free property.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/jcm.2404-m2023-0250

Journal of Computational Mathematics, Vol. 43 (2025), Iss. 4 : pp. 898–917

Published online:    2025-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    20

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

Author Details

Yue Wang

Fuzheng Gao