AI 中文总结
该研究将二维奇异Zienkiewicz元扩展至三维，构建了基于有理形函数的H²协调有限元，开发了对应有理函数的精确迭代积分程序，实现了有限元相关项的精确积分。
AI 中文摘要
我们将二维奇异Zienkiewicz元扩展至三维，基于有理形函数在四面体网格上构建了一种新型H²协调有限元。除有限元构造及其协调性分析外，我们还开发了针对此类有理函数的精确迭代积分程序，所得公式可精确积分基函数、其导数及有限元组装中出现的乘积项。
英文摘要
We extend the two-dimensional singular Zienkiewicz element to three dimensions, leading to a novel $H^2$-conforming finite element on tetrahedral meshes based on rational shape functions. Besides the finite element construction and its conformity analysis, we develop an exact iterative integration procedure for the associated class of rational functions. The resulting formulae allow for the exact integration of the basis functions, their derivatives, and the products occurring in finite element assembly.
