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

03/27/2021 ∙ by Jun Hu, et al. ∙ 0

This paper proposes a construction of local C^r interpolation spaces and C^r conforming finite element spaces with arbitrary r in any dimension. It is shown that if k ≥ 2^dr+1 the space 𝒫_k of polynomials of degree ≤ 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. It solves a long-standing open problem in finite element methods.

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