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

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(d)r+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