Error analysis of a fractional-step method for magnetohydrodynamics equations

This paper focuses on a fractional-step finite element method for the magnetohydrodynamics problems in three-dimensional bounded domains. It is shown that the proposed fractional-step scheme allows for a discrete energy identity. A rigorous error analysis is presented. We derive the temporal and spatial error estimates of O(Δt+h) for the velocity and the magnetic field in the discrete space l2(H1)∩l∞(L2) under the constraint Δt≥Ch.