A Construction of Cr Conforming Finite Element Spaces in Any Dimension

Abstract

This paper proposes a construction of Cr conforming finite element spaces with arbitrary r in any dimension. It is shown that if k 2dr+1 the space Pk of polynomials of degree k can be taken as the shape function space of Cr finite element spaces in d dimensions. This is the first work on constructing such Cr 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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