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.
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