This work gives the high accuracy analysis of a rectangular biharmonic element in arbitrarily high‐dimensional cases. Given an n‐rectangle, we construct the nonconforming finite element and show its explicit standard basis representation. We prove that, if the n‐rectangular mesh is uniform, this element can achieve a second order convergence rate in energy norm when applied to biharmonic problems. Numerical examples for n = 3 are also presented.

中文翻译：

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n矩形网格上的高精度非协调双调和单元

这项工作可以在任意高维情况下对矩形双谐波元件进行高精度分析。给定一个n矩形，我们构造不合格的有限元并显示其显式的标准基表示。我们证明，如果n矩形网格是均匀的，则该元素在应用于双调和问题时可以在能量范数上达到二阶收敛速度。 还给出了n = 3的数值示例。