非线性弹性问题的增强混合有限元方法

本文介绍和分析了一类具有强对称应力张量的非线性弹性问题的全增强混合有限元方法。这种方法除了包括通常线弹性问题 中的应力张量和位移外，还把应变张量作为辅助未知量。通过引入迦辽金最小二乘项，我们得到了两层鞍点算子方程来作为我们的结果弱方程。为了得到离散增强方程的适定性，我们采用分片常量多项式去逼近应变张量和分片线性多项式去逼近应力张量和位移，并且我们也得到了最优阶误差估计。最后，数值例子验证我们的理论分析。

An augmented mixed finite element method for nonlinear elasticity problems

In this paper, we introduce and analyse a full augmented mixed finite element methods for a class of nonlinear elasticity problems with strongly imposed symmetry stress tensor. The mixed method includes the strain tensor as an auxiliary unknown, which combines with the usual stress-displacement approach adopted in linear elasticity. This approach leads to twofold saddle point operator equation as the resulting weak formulation. Then, we adopt the piecewise constant finite element to approximate the strain tensor and piecewise linear continuous polynomial to approximate the stress tensor and displacement so that we obtain the well-posed of augmented scheme and the optimal error estimate. Finally, the numerical example are presented to confirm our theoretical analysis.