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Volume 16, Issue 2
Mixed Finite Element Methods for the Ferrofluid Model with Magnetization Paralleled to the Magnetic Field

Yongke Wu & Xiaoping Xie

DOI: 10.4208/nmtma.OA-2022-0163

Numer. Math. Theor. Meth. Appl., 16 (2023), pp. 489-510.

Published online: 2023-04

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  • 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.

  • Keywords

Ferrofluid flow, decoupled system, mixed finite element method, error estimate.

  • AMS Subject Headings

65N55, 65F10, 65N22, 65N30

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{NMTMA-16-489, author = {Wu , Yongke and Xie , Xiaoping}, title = {Mixed Finite Element Methods for the Ferrofluid Model with Magnetization Paralleled to the Magnetic Field}, journal = {Numerical Mathematics: Theory, Methods and Applications}, year = {2023}, volume = {16}, number = {2}, pages = {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.

}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.OA-2022-0163}, url = {http://global-sci.org/intro/article_detail/nmtma/21586.html} }
TY - JOUR T1 - Mixed Finite Element Methods for the Ferrofluid Model with Magnetization Paralleled to the Magnetic Field AU - Wu , Yongke AU - Xie , Xiaoping JO - Numerical Mathematics: Theory, Methods and Applications VL - 2 SP - 489 EP - 510 PY - 2023 DA - 2023/04 SN - 16 DO - http://doi.org/10.4208/nmtma.OA-2022-0163 UR - https://global-sci.org/intro/article_detail/nmtma/21586.html KW - Ferrofluid flow, decoupled system, mixed finite element method, error estimate. AB -

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.

Wu , Yongke and Xie , Xiaoping. (2023). Mixed Finite Element Methods for the Ferrofluid Model with Magnetization Paralleled to the Magnetic Field. Numerical Mathematics: Theory, Methods and Applications. 16 (2). 489-510. doi:10.4208/nmtma.OA-2022-0163
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