Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the Existence Uniqueness and Numerical Computation of Non-linear
  Coupled Elliptic PDE System with its application   In this study we prove the existence-uniqueness of a coupled non-linear
elliptic PDE system using Lax-Milgram theorem, Galerkin Method, Brouwer's fixed
point theorem. Later we derive the finite element scheme for the numerical
solution of the PDE system and also carry out the convergence analysis for the
derived scheme. Further successfully apply the scheme to an application related
to free convection phenomena.

14
The categories of this paper are: math-ph
0
The categories of this paper are: hep-ph
30
The categories of this paper are: q-alg
17
The categories of this paper are: q-fin
7
The categories of this paper are: hep-th
27
The categories of this paper are: comp-gas
22
The categories of this paper are: chao-dyn
37
The categories of this paper are: supr-con
15
The categories of this paper are: nucl-ex
34
The categories of this paper are: chem-ph
5
The categories of this paper are: gr-qc
32
The categories of this paper are: atom-ph
25
The categories of this paper are: patt-sol
28
The categories of this paper are: alg-geom
20
The categories of this paper are: acc-phys
4
The categories of this paper are: cond-mat