Decoupled, semi-implicit scheme for a coupled system arising in magnetohydrodynamics problem

In this paper, we focus on a decoupled, linearized semi-implicit Galerkin FEM scheme for a MHD system coupled by the time-dependent Navier-Stokes equation with the steady Maxwell's equations in three-dimensional convex domain. First, additional regularities of the solution to the coupled MHD system are derived. By using H1-conforming finite element to approximate the magnetic field, it is shown that the proposed semi-linearized scheme is of the first-order convergence order of the velocity field, the magnetic field and the pressure under the time step condition Δt=O(h).