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

2021/03/27 by Hu, Jun, Lin, Ting, Wu, Qingyu · 4 citations
#65N30 #FOS: Mathematics #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.2103.14924

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 ≥ 2^dr+1 the space \mathcal 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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