TY - JOUR
T1 - Error Analysis of a New Euler Semi-Implicit Time-Discrete Scheme for the Incompressible MHD System with Variable Density
AU - Li , Yuan
AU - Cui , Xuewei
JO - Advances in Applied Mathematics and Mechanics
VL - 1
SP - 263
EP - 294
PY - 2024
DA - 2024/12
SN - 17
DO - http://doi.org/10.4208/aamm.OA-2023-0025
UR - https://global-sci.org/intro/article_detail/aamm/23602.html
KW - Magnetohydrodynamics, variable density flows, Euler semi-implicit scheme, error analysis.
AB - <p style="text-align: justify;">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 $\tau&gt;0.$ 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.</p>