Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Construction of $C^r$ Conforming Finite Element Spaces in Any
  Dimension   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 $k \ge 2^{d}r+1$ 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.

25
The categories of this paper are: patt-sol
13
The categories of this paper are: quant-ph
32
The categories of this paper are: atom-ph
31
The categories of this paper are: ao-sci
23
The categories of this paper are: solv-int
29
The categories of this paper are: funct-an
6
The categories of this paper are: astro-ph
33
The categories of this paper are: plasm-ph
30
The categories of this paper are: q-alg
24
The categories of this paper are: dg-ga
9
The categories of this paper are: nlin
35
The categories of this paper are: mtrl-th
0
The categories of this paper are: hep-ph
21
The categories of this paper are: adap-org
4
The categories of this paper are: cond-mat
34
The categories of this paper are: chem-ph