Year: 2025
Author: Lina Ma, Cheng Wang, Zeyu Xia
Advances in Applied Mathematics and Mechanics, Vol. 17 (2025), Iss. 2 : pp. 633–662
Abstract
In this paper we propose and analyze a numerical scheme coupling a second-order backward differential formulation (BDF) and the finite element method (FEM) to solve the incompressible resistive magnetohydrodynamic (MHD) equations. In the discrete scheme, the pressure variable in the fluid field equation is computed through a Poisson equation, and a linear and decoupled method is adopted to separate both the magnetic and the fluid field functions from the original system. As a result, the original system is divided into several sub-systems for which the numerical solutions can be obtained efficiently. We prove the unique solvability, the unconditional energy stability, and particularly optimal error estimates for the proposed scheme. Numerical results are presented to validate the theory of the scheme.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/aamm.OA-2023-0118
Advances in Applied Mathematics and Mechanics, Vol. 17 (2025), Iss. 2 : pp. 633–662
Published online: 2025-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 30
Keywords: Resistive MHD equations finite element methods BDF decoupled scheme unconditional energy stability optimal error estimates.