Decoupled schemes for unsteady MHD equations II: Finite element spatial discretization and numerical implementation

In this article, a decoupled fully discrete scheme for solving 2D magnetohydrodynamics (MHD) equations is proposed. The decoupled scheme is used for time discretization, and the finite element method is used for spatial discretization. Firstly, the almost unconditional stability (Δt≤C) of this scheme is established. Then optimal L2L2 and H1H1 error estimates of numerical solution are provided. Finally, a numerical example is presented to confirm our theoretical results and show the high efficiency of the decoupled scheme.