A Construction of $C^r$ Conforming Finite Element Spaces in Any Dimension
- Resource Type
- Working Paper
- Authors
- Hu, Jun; Lin, Ting; Wu, Qingyu
- Source
- Subject
- Mathematics - Numerical Analysis
65N30
- Language
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. It solves a long-standing open problem in finite element methods.
Comment: 25 pages, 5 figures