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).
Author NameAffiliation
Yanping SUN College of Science, Henan University of Engineering, Henan 451191, P. R. China 
Tao SUN School of Statistics and Mathematics, Shanghai Lixin University of Accounting and Finance, Shanghai 201209, P. R. China 
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      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 inf-sup 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.
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