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Volume 17, Issue 1
Error Analysis of a New Euler Semi-Implicit Time-Discrete Scheme for the Incompressible MHD System with Variable Density

Yuan Li & Xuewei Cui

Adv. Appl. Math. Mech., 17 (2025), pp. 263-294.

Published online: 2024-12

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  • 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.

  • AMS Subject Headings

65N30, 76M05

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COPYRIGHT: © Global Science Press

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@Article{AAMM-17-263, author = {Li , Yuan and Cui , Xuewei}, title = {Error Analysis of a New Euler Semi-Implicit Time-Discrete Scheme for the Incompressible MHD System with Variable Density}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2024}, volume = {17}, number = {1}, pages = {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.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.OA-2023-0025}, url = {http://global-sci.org/intro/article_detail/aamm/23602.html} }
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 -

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.

Li , Yuan and Cui , Xuewei. (2024). 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. 17 (1). 263-294. doi:10.4208/aamm.OA-2023-0025
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