Adv. Appl. Math. Mech., 17 (2025), pp. 263-294.
Published online: 2024-12
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The incompressible magnetohydrodynamics system with variable density is coupled by the incompressible Navier-Stokes equations with variable density and the Maxwell equations. In this paper, we study a new first-order Euler semi-discrete scheme for solving this system. The proposed numerical scheme is unconditionally stable for any time step size $\tau>0.$ Furthermore, a rigorous error analysis is presented and the first-order temporal convergence rate $\mathcal{O}(\tau)$ is derived by using the method of mathematical induction and the discrete maximal $L^p$-regularity of the Stokes problem. Finally, numerical results are given to support the theoretical analysis.
}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.OA-2023-0025}, url = {http://global-sci.org/intro/article_detail/aamm/23602.html} }The incompressible magnetohydrodynamics system with variable density is coupled by the incompressible Navier-Stokes equations with variable density and the Maxwell equations. In this paper, we study a new first-order Euler semi-discrete scheme for solving this system. The proposed numerical scheme is unconditionally stable for any time step size $\tau>0.$ Furthermore, a rigorous error analysis is presented and the first-order temporal convergence rate $\mathcal{O}(\tau)$ is derived by using the method of mathematical induction and the discrete maximal $L^p$-regularity of the Stokes problem. Finally, numerical results are given to support the theoretical analysis.