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<p>In this paper, we propose a fully discrete finite element method for an incompressible ferrohydrodynamics flow. The constitutive equation we consider, proposed by Rosensweig (2002), models the motion of a magnetic fluid. We develop a semi-implicit, energy-stable scheme to solve this nonlinear system. Using the Leray-Schauder fixed point theorem, we establish the existence and uniqueness of the numerical solutions. Additionally, we prove the unconditional convergence of the numerical scheme through the Aubin-Lions-Simon lemma. Numerical experiments are conducted to verify the convergence of our scheme and to simulate the behavior of ferrohydrodynamic flows.</p>

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On the Rosensweig model: A linear, energy-stable, and convergent finite element method

  • 期刊论文

  • 发表日期：

    2025年7月24日

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  • Xiaojing Dong,
  • Huayi Huang,
  • Yunqing Huang,
  • Qili Tang

摘要

In this paper, we propose a fully discrete finite element method for an incompressible ferrohydrodynamics flow. The constitutive equation we consider, proposed by Rosensweig (2002), models the motion of a magnetic fluid. We develop a semi-implicit, energy-stable scheme to solve this nonlinear system. Using the Leray-Schauder fixed point theorem, we establish the existence and uniqueness of the numerical solutions. Additionally, we prove the unconditional convergence of the numerical scheme through the Aubin-Lions-Simon lemma. Numerical experiments are conducted to verify the convergence of our scheme and to simulate the behavior of ferrohydrodynamic flows.