This paper proposes a construction of \(C^r\) conforming finite element spaces with arbitrary r in any dimension. It is shown that if \(k \ge 2^{d}r+1\) the space \({\mathcal {P}}_k\) of polynomials of degree \(\le k\) can be taken as the shape function space of \(C^r\) finite element spaces in d dimensions. This is the first work on constructing such \(C^r\) conforming finite elements in any dimension in a unified way.

中文翻译：

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任意维 $$C^r$$ 相容有限元空间的构造

本文提出了在任意维度上构造任意r的\(C^r\)符合有限元空间。结果表明，如果\(k \ge 2^{d}r+1\)次数为 \ (\le k \)的多项式的空间\({\mathcal {P}}_k \)可以看作d维\(C^r\)有限元空间的形函数空间。这是第一个以统一的方式构造任意维度的\(C^r\)符合有限元的工作。