Mixed Finite Element Methods for the Ferrofluid Model with Magnetization Paralleled to the Magnetic Field

Mixed Finite Element Methods for the Ferrofluid Model with Magnetization Paralleled to the Magnetic Field

Year:    2023

Author:    Yongke Wu, Xiaoping Xie

Numerical Mathematics: Theory, Methods and Applications, Vol. 16 (2023), Iss. 2 : pp. 489–510

Abstract

Mixed finite element methods are considered for a ferrofluid flow model with magnetization paralleled to the magnetic field. The ferrofluid model is a coupled system of the Maxwell equations and the incompressible Navier-Stokes equations. By skillfully introducing some new variables, the model is rewritten as several decoupled subsystems that can be solved independently. Mixed finite element formulations are given to discretize the decoupled systems with proper finite element spaces. Existence and uniqueness of the mixed finite element solutions are shown, and optimal order error estimates are obtained under some reasonable assumptions. Numerical experiments confirm the theoretical results.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/nmtma.OA-2022-0163

Numerical Mathematics: Theory, Methods and Applications, Vol. 16 (2023), Iss. 2 : pp. 489–510

Published online:    2023-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    22

Keywords:    Ferrofluid flow decoupled system mixed finite element method error estimate.

Author Details

Yongke Wu

Xiaoping Xie

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