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Convergence Analysis of the Fully Discrete Projection Method for Inductionless Magnetohydrodynamics System Based on Charge Conservation

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Abstract

In this paper, we focus on a finite element projection method for inductionless magnetohydrodynamics equations. A fully discrete projection method based on Euler semi-implicit scheme is proposed in which continuous elements are used to approximate the Navier–Stokes equations and the divergence-conforming element is used to approximate the current density. The key of the projection method is that it must be compatible with two different spaces for calculating velocity, which leads to solve the pressure by solving a Poisson equation. The results show that the proposed projection scheme meets a discrete energy stability and the discrete current density keeps charge conservation property. In addition, this paper provides a rigorous optimal error analysis of velocity, pressure and current density. Finally, several numerical examples are performed to demonstrate both accuracy and efficiency of our proposed scheme.

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Funding

This work is supported by the Natural Science Foundation of China (12201353), Program for IRTSTHN (22IRTSTHN013), Shandong Province Natural Science Foundation (ZR2021QA054) and the Talent Fund of Beijing Jiaotong University (2023XKRC024).

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Authors and Affiliations

  1. College of Mathematics and Information Science, Henan University of Economics and Law, Zhengzhou, 450045, China

    Xiaonian Long

  2. School of Mathematics and Statistics, Beijing Jiaotong University, Beijing, 100044, China

    Qianqian Ding

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  1. Xiaonian Long
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Correspondence to Qianqian Ding.

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Long, X., Ding, Q. Convergence Analysis of the Fully Discrete Projection Method for Inductionless Magnetohydrodynamics System Based on Charge Conservation. J Sci Comput 96, 2 (2023). https://doi.org/10.1007/s10915-023-02226-1

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