Parameter dependent finite element analysis for ferronematics solutions

This paper focuses on the analysis of a free energy functional, that models dilute suspension magnetic nanoparticles in two-dimensional nematic well. The first part article is devoted to asymptotic global minimizers limit vanishing elastic constant, ℓ→0 where re-scaled constant ℓ inversely proportional domain area. results concern strong H1-convergence and ℓ-independent H2-bound for smooth bounded 2D domains, with boundary topologically trivial Dirichlet conditions. second discrete approximation regular solutions corresponding non-linear system partial differential equations cubic non-linearity non-homogeneous We establish (i) existence local uniqueness using fixed point argument, (ii) best result norm, (iii) error estimates L2 norms ℓ-discretization parameter dependency conforming finite element method. Finally, theoretical are complemented by numerical experiments solution profiles, convergence rates corroborates estimates, followed plots illustrate dependence discretization ℓ.