Parameter dependent finite element analysis for ferronematics solutions

Maity, Ruma Rani and Majumdar, Apala and Nataraj, Neela (2021) Parameter dependent finite element analysis for ferronematics solutions. Computers and Mathematics with Applications, 103. pp. 127-155. ISSN 0898-1221 (https://doi.org/10.1016/j.camwa.2021.10.027)

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Abstract

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, ℓ→0 where the re-scaled elastic constant ℓ is inversely proportional to the domain area. The first results concern the strong H1-convergence and a ℓ-independent H2-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 L2 norms with ℓ- 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 ℓ.

ORCID iDs

Maity, Ruma Rani, Majumdar, Apala ORCID logoORCID: https://orcid.org/0000-0003-4802-6720 and Nataraj, Neela;
  • Item type:Article
    ID code:78478
    Dates:
    Date
    Event
    1 December 2021
    Published
    8 November 2021
    Published Online
    23 October 2021
    Accepted
    Subjects:Science > Mathematics
    Department:Faculty of Science > Mathematics and Statistics
    Depositing user: Pure Administrator
    Date deposited:10 Nov 2021 11:15
    Last modified:11 Nov 2024 13:17
    URI:https://strathprints.strath.ac.uk/id/eprint/78478
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