A Stabilized Formulation for Linear Elasticity Equation with Weakly Symmetric Stress 
Received:August 09, 2022 Revised:January 08, 2023 
Key Words:
mixed finite element method stabilized formulation linear elasticity equation weakly symmetric stress

Fund Project:Supported by the National Natural Science Foundation of China (Grant No.12171141), the Key Scientific Research Projects of Colleges and Universities in Henan Province (Grant No.23B110005), the Young Natural Science Foundation of Henan Province (Grant No.222300420135) and the Doctoral Fund of Henan University of Engineering (Grant No.D2017022). 

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Abstract: 
The linear elastic problem with weak symmetric stress obtained by Lagrange multiplier method is discussed by using the stabilization method. The stress and displacement of the variational problem are approximated by linear element and piecewise constant. By adding stabilization terms $G_1(\cdot,\cdot), G_2(\cdot,\cdot)$ and $G_3(\cdot,\cdot)$, the corresponding mixed discrete variational problem satisfies the weak infsup condition. Then the error estimation between the solution of the variational problem and the stabilized mixed finite element solution is studied in detail. Finally, two numerical examples are used to verify the effectiveness of the theoretical analysis. 
Citation: 
DOI:10.3770/j.issn:20952651.2023.03.009 
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