发表机构
Politecnico di Torino（都灵理工大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
将拉链有限元方法推广至三维多面体网格，通过局部子四面体化构造高阶形函数，并引入更稳健的QR策略替代启发式方法，数值测试验证了最优收敛阶。
AI 中文摘要
我们将高阶拉链有限元方法扩展到三维多面体单元。该构造依赖于通过三角剖分多边形面并将所得顶点连接到合适的内部点而获得的局部子四面体化。高阶形函数被构造为标准有限元基函数的线性组合，其系数经过选择以确保在面和多面体内部精确重现多项式，同时保持全局C0连续性。我们进一步引入了一种基于QR分解的策略，作为二维情形下所采用的启发式程序的系统性替代方案。QR策略比启发式策略更系统、更稳健，且独立于空间维度，避免了几何对齐测试和依赖问题的容差。所得方法针对扩散-反应问题进行了公式化，并通过三维收敛测试进行了数值评估，确认了预期的多项式阶最优精度。
英文摘要
We extend the high-order Zipped Finite Element Method to three-dimensional polyhedral elements. The construction relies on a local sub-tetrahedralization obtained by triangulating the polygonal faces and connecting the resulting vertices to a suitable interior point. High-order shape functions are constructed as linear combinations of standard finite element basis functions, with coefficients chosen to ensure exact polynomial reproduction on the faces and in the element interior while preserving global C0-conformity. We further introduce a QR-based strategy as a systematic alternative to the heuristic procedure that was adopted for the two-dimensional case. The QR-strategy is more systematic and robust than the heuristic strategy, while being independent of the spatial dimension and avoiding geometric alignment tests and problem-dependent tolerances. The resulting method is formulated for a diffusion-reaction problem and numerically assessed through three-dimensional convergence tests, confirming the expected optimal polynomial order of accuracy.
