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 - <p style="text-align: justify;">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.</p>