一种用于非线性弹性中空化计算的二次等参数FEM网格策略
A Meshing Strategy for a Quadratic Iso-parametric FEM in Cavitation Computation in Nonlinear Elasticity
AI总结：
本文分析了二次等参数有限元方法在典型空化问题中的近似性质，提出基于误差等分布原理的网格分布策略，并证明了有限元空化解的收敛性，数值实验验证了最优收敛率的实现。
摘要：
本文分析了二次等参数有限元方法在典型空化问题中的近似性质，提出基于误差等分布原理的网格分布策略，并证明了有限元空化解的收敛性，数值实验验证了最优收敛率的实现。
英文摘要：
The approximation properties of a quadratic iso-parametric finite element method for a typical cavitation problem in nonlinear elasticity are analyzed. More precisely, (1) the finite element interpolation errors are established in terms of the mesh parameters; (2) a mesh distribution strategy based on an error equi-distribution principle is given; (3) the convergence of finite element cavity solutions is proved. Numerical experiments show that, in fact, the optimal convergence rate can be achieved by the numerical cavity solutions.
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