Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Stability of Hodge decompositions in finite element spaces of
  differential forms in arbitrary dimension   We elaborate on the interpretation of some mixed finite element spaces in
terms of differential forms. First we develop a framework in which we show how
tools from algebraic topology can be applied to the study of their
cohomological properties. The analysis applies in particular to certain $hp$
finite element spaces, extending results in trivial topology often referred to
as the exact sequence property. Then we define regularization operators.
Combined with the standard interpolators they enable us to prove discrete
Poincar\'e-Friedrichs inequalities and discrete Rellich compactness for finite
element spaces of differential forms of arbitrary degree on compact manifolds
of arbitrary dimension.

22
The categories of this paper are: chao-dyn
15
The categories of this paper are: nucl-ex
33
The categories of this paper are: plasm-ph
36
The categories of this paper are: cmp-lg
0
The categories of this paper are: hep-ph
4
The categories of this paper are: cond-mat
19
The categories of this paper are: eess
24
The categories of this paper are: dg-ga
25
The categories of this paper are: patt-sol
35
The categories of this paper are: mtrl-th
29
The categories of this paper are: funct-an
31
The categories of this paper are: ao-sci
14
The categories of this paper are: math-ph
30
The categories of this paper are: q-alg
34
The categories of this paper are: chem-ph
32
The categories of this paper are: atom-ph