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A Construction of \(C^r\) Conforming Finite Element Spaces in Any Dimension

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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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Authors and Affiliations

  1. LMAM and School of Mathematical Sciences, Peking University, Beijing, 100871, China

    Jun Hu

  2. School of Mathematical Sciences, Peking University, Beijing, 100871, China

    Ting Lin & Qingyu Wu

Authors
  1. Jun Hu
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  2. Ting Lin
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  3. Qingyu Wu
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Correspondence to Jun Hu.

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Communicated by Rob Stevenson.

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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

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