Temporal convergence analysis of an energy preserving projection method for a coupled magnetohydrodynamics equations

Abstract

In this paper, we study and analyze a semi-discrete projection scheme for solving a hybrid magnetohydrodynamics equations coupled by the nonstationary Navier–Stokes equations and the stationary Maxwell equations. The suggested projection scheme is energy preserving and satisfies the divergence free condition of the velocity field at the discrete level. As the time step size is sufficiently small, we establish optimal temporal error estimates under some regularity assumptions. Numerical results are provided to show the efficiency of the suggested scheme and verify the theoretical analysis.