| 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. |
