Error Analysis of a New Euler Semi-Implicit Time-Discrete Scheme for the Incompressible MHD System with Variable Density
Year: 2025
Author: Yuan Li, Xuewei Cui
Advances in Applied Mathematics and Mechanics, Vol. 17 (2025), Iss. 1 : pp. 263–294
Abstract
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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/aamm.OA-2023-0025
Advances in Applied Mathematics and Mechanics, Vol. 17 (2025), Iss. 1 : pp. 263–294
Published online: 2025-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 32
Keywords: Magnetohydrodynamics variable density flows Euler semi-implicit scheme error analysis.