Abstract
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.
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Hu, J., Lin, T. & Wu, Q. A Construction of \(C^r\) Conforming Finite Element Spaces in Any Dimension. Found Comput Math (2023). https://doi.org/10.1007/s10208-023-09627-6
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DOI: https://doi.org/10.1007/s10208-023-09627-6