Error Analysis of a New Euler Semi-Implicit Time-Discrete Scheme for the Incompressible MHD System with Variable Density (Advances in Applied Mathematics and Mechanics, 2024)
The incompressible magnetohydrodynamics system with variable densityis coupled by the incompressible Navier-Stokes equations with variable density andthe Maxwell equations. In this paper, we study a new first-order Euler semi-discretescheme for solving this system. The proposed numerical scheme is unconditionallystable for any time step size $τ>0.$ Furthermore, a rigorous error analysis is presentedand the first-order temporal convergence rate $\mathcal{O}(τ)$ is derived by using the method ofmathematical induction and the discrete maximal $L^p$-regularity of the Stokes problem.Finally, numerical results are given to support the theoretical analysis.