具有弱对称应力的线弹性方程的稳定化格式

A Stabilized Formulation for Linear Elasticity Equation with Weakly Symmetric Stress

中文关键词:  混合有限元方法  稳定化格式  线弹性方程  弱对称应力

英文关键词:mixed finite element method  stabilized formulation  linear elasticity equation  weakly symmetric stress

中文摘要:

      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.

英文摘要:

      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.