10th March – ‪Ruma Maity: Parameter dependent finite element analysis for ferronematics solutions

In this talk, we focus on the analysis of a free energy functional, that models a dilute suspension of magnetic nanoparticles in a two-dimensional nematic well, referred to as ferronematics. We discuss the asymptotic analysis of global energy minimizers in the limit of vanishing elastic constant, where the re-scaled elastic constant l is inversely proportional to the domain area. The conforming finite element method is used to approximate the regular solutions of the corresponding non-linear system of partial differential equations with cubic nonlinearity and non-homogeneous Dirichlet boundary conditions. We establish the existence and local uniqueness of the discrete solutions, error estimates in the energy and L2 norms with l- discretization parameter dependency. The theoretical results are complemented by the numerical experiments on the discrete solution profiles, and the numerical convergence rates that corroborate the theoretical estimates.