Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Decoupling of Mixed Methods Based on Generalized Helmholtz
  Decompositions   A framework to systematically decouple high order elliptic equations into
combination of Poisson-type and Stokes-type equations is developed. The key is
to systematically construct the underling commutative diagrams involving the
complexes and Helmholtz decompositions in a general way. Discretizing the
decoupled formulation leads to a natural superconvergence between the Galerkin
projection and the decoupled approximation. Examples include but not limit to:
the primal formulations and mixed formulations of biharmonic equation, fourth
order curl equation, and triharmonic equation etc. As a by-product, Helmholtz
decompositions for many dual spaces are obtained.

13
The categories of this paper are: quant-ph
8
The categories of this paper are: hep-ex
16
The categories of this paper are: stat
35
The categories of this paper are: mtrl-th
7
The categories of this paper are: hep-th
25
The categories of this paper are: patt-sol
30
The categories of this paper are: q-alg
12
The categories of this paper are: nucl-th
33
The categories of this paper are: plasm-ph
21
The categories of this paper are: adap-org
15
The categories of this paper are: nucl-ex
18
The categories of this paper are: econ
22
The categories of this paper are: chao-dyn
19
The categories of this paper are: eess
0
The categories of this paper are: hep-ph
4
The categories of this paper are: cond-mat