| 具有弱对称应力的线弹性方程的稳定化格式 |
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| 引用本文： | 孙艳萍,孙涛.具有弱对称应力的线弹性方程的稳定化格式[J].数学研究及应用,2023,43(3):350-362. |
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| 作者姓名： | 孙艳萍 孙涛 |
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| 作者单位： | 河南工程学院理学院, 河南 郑州 451191;上海立信会计金融学院统计与数学学院, 上海 201209 |
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| 基金项目： | 国家自然科学基金(Grant No.12171141), 河南省高等学校重点科研项目(Grant No.23B110005), 河南省青年自然科学基金(Grant No.222300420135), 河南工程学院博士基金(Grant No.D2017022). |
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| 摘 要： | 利用稳定化方法讨论拉格朗日乘子法得到的具有弱对称应力的线弹性问题. 用线性元和分片常数分别逼近变分问题的应力和位移. 并通过添加稳定项$G_1(\cdot,\cdot)$, $G_2(\cdot,\cdot)$和$G_3(\cdot,\cdot)$ 使相应混合离散变分问题满足弱BB条件. 接着详细研究了变分问题的解与稳定混合有限元解之间的误差估计,最后用两个数值算例验证理论分析的有效性.
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| 关 键 词： | 混合有限元方法 稳定化格式 线弹性方程 弱对称应力 |
| 收稿时间： | 2022/8/9 0:00:00 |
| 修稿时间： | 2023/1/8 0:00:00 |
A Stabilized Formulation for Linear Elasticity Equation with Weakly Symmetric Stress |
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| Yanping SUN,Tao SUN.A Stabilized Formulation for Linear Elasticity Equation with Weakly Symmetric Stress[J].Journal of Mathematical Research with Applications,2023,43(3):350-362. |
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| Authors: | Yanping SUN Tao SUN |
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| Institution: | College of Science, Henan University of Engineering, Henan 451191, P. R. China; School of Statistics and Mathematics, Shanghai Lixin University of Accounting and Finance, Shanghai 201209, P. R. China |
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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 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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| Keywords: | mixed finite element method stabilized formulation linear elasticity equation weakly symmetric stress |
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