Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Parameter dependent finite element analysis for ferronematics solutions   This paper focuses on the analysis of a free energy functional, that models a
dilute suspension of magnetic nanoparticles in a two-dimensional nematic well.
The {\it first part} of the article is devoted to the asymptotic analysis of
global energy minimizers in the limit of vanishing elastic constant, $\ell
\rightarrow 0$ where the re-scaled elastic constant $\ell$ is inversely
proportional to the domain area. The first results concern the strong
$H^1$-convergence and a $\ell$-independent $H^2$-bound for the global
minimizers on smooth bounded 2D domains, with smooth boundary and topologically
trivial Dirichlet conditions. The {\it second part} focuses on the discrete
approximation of regular solutions of the corresponding non-linear system of
partial differential equations with cubic non-linearity and non-homogeneous
Dirichlet boundary conditions. We establish (i) the existence and local
uniqueness of the discrete solutions using fixed point argument, (ii) a best
approximation result in energy norm, (iii) error estimates in the energy and
$L^2$ norms with $\ell $- discretization parameter dependency for the
conforming finite element method. Finally, the theoretical results are
complemented by numerical experiments on the discrete solution profiles, the
numerical convergence rates that corroborates the theoretical estimates,
followed by plots that illustrate the dependence of the discretization
parameter on $\ell$.

14
The categories of this paper are: math-ph
33
The categories of this paper are: plasm-ph
16
The categories of this paper are: stat
22
The categories of this paper are: chao-dyn
18
The categories of this paper are: econ
5
The categories of this paper are: gr-qc
29
The categories of this paper are: funct-an
37
The categories of this paper are: supr-con
9
The categories of this paper are: nlin
11
The categories of this paper are: hep-lat
24
The categories of this paper are: dg-ga
0
The categories of this paper are: hep-ph
20
The categories of this paper are: acc-phys
17
The categories of this paper are: q-fin
27
The categories of this paper are: comp-gas
21
The categories of this paper are: adap-org