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Convergence Analysis of a BDF Finite Element Method for the Resistive Magnetohydrodynamic Equations

Convergence Analysis of a BDF Finite Element Method for the Resistive Magnetohydrodynamic Equations

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.

Author Details

Lina Ma

Cheng Wang

Zeyu Xia