Mixed finite element methods for the ferrofluid model with magnetization paralleled to the magnetic field
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
Cite
@article{arxiv.2208.05118,
title = {Mixed finite element methods for the ferrofluid model with magnetization paralleled to the magnetic field},
author = {Yongke Wu and Xiaoping Xie},
journal= {arXiv preprint arXiv:2208.05118},
year = {2022}
}
Comments
arXiv admin note: text overlap with arXiv:2206.03129