Research On The Second-order BDF Galerkin Finite Element Scheme For A Hybrid MHD System

In this paper,a second-order backward differentiation formula(BDF)scheme for a hybrid MHD system is considered.Being different with the steady and nonstationary MHD equations,the hybrid MHD system is coupled by the time-dependent Navier-Stokes equations and the steady Maxwell equations.The article is divided into three parts.1.First,the BDF scheme is decoupled and linear.Because it is decoupled,we can solve the magnetic field and then solve the velocity and pressure fields.Then,the linearization scheme based on extrapolation is used to linearize the nonlinear term,which avoids iterations in the same time layer and saves calculation time.2.Secondly,we proved the unconditionally optimal second-order convergence O(h2+(?t)2)under the L2 norm,and gave the time and space error estimates of the magnetic field,velocity field and pressure field.3.Finally,numerical results are used to verify the theoretical results.