In this paper, we present the numerical analysis on high order dual parametric finite element methods for the cavitation computation problems in nonlinear elasticity, which leads to a meshing strategy assuring high efficiency on numerical approximations to cavity deformations. Furthermore, to cope with the high order approximation of the finite element methods, properly chosen weighted Gaussian type numerical quadrature is applied to the singular part of the elastic energy. Our numerical experiments show that the high order dual parametric finite element methods work well when coupled with properly designed weighted Gaussian type numerical quadratures for the singular part of the elastic energy, and the convergence rates of the numerical cavity solutions are shown to be significantly improved as expected.

中文翻译：

---

非线性弹性中气穴计算的高阶双参数有限元方法

在本文中，我们对非线性弹性中的气穴计算问题进行了高阶双参数有限元方法的数值分析，这导致了一种网格划分策略，可确保在对腔体变形进行数值逼近时确保高效。此外，为了应付的有限元方法中的高次近似，适当地选择加权的高斯型数值积分被施加到弹性能量的单数部分。我们的数值实验表明，高阶对偶参数有限元方法与弹性能量奇异部分的适当设计的加权高斯型数值正交函数相结合时效果很好，并且数值腔解的收敛速度显着提高。预期。