  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 $\ell$.
