Unconditional optimal first-order error estimates of a full pressure segregation scheme for the magnetohydrodynamics equations

In this article, a first-order linear fully discrete pressure segregation scheme is studied for the time-dependent incompressible magnetohydrodynamics (MHD) equations in three-dimensional bounded domain. Based on an incremental pressure projection method, this scheme allows us to decouple the MHD system into two sub-problems at each time step, one is the velocity-magnetic field system, the other is the pressure system. Firstly, a coupled linear elliptic system is solved for the velocity and the magnetic field. Next, a Poisson-Neumann problem is treated for the pressure. We analyze the temporal error and the spatial error, respectively, and derive the temporal-spatial error estimates of O(Delta t + h) for the velocity and the magnetic field in the discrete space l(infinity)(H-1) and for the pressure in the discrete space l(infinity)(L-2) without imposing constraints on the mesh width h and the time step size Delta t. Finally, some numerical results are presented to confirm the theoretical predictions and demonstrate the efficiency of the method.