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A second-order scheme based on blended BDF for the incompressible MHD system

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Abstract

For the incompressible MHD equations, we present a fully discrete second-order-in-time scheme based on a blended BDF and extrapolation treatments for nonlinear terms. The proposed scheme is more accurate than the two-step BDF with additional nominal computational time and is still A-stable. Then, unconditional stability, long-time stability, and optimal convergence rate of the scheme are presented. At last, the numerical findings are verified by comparison with the two-step BDF scheme in several 2D and 3D numerical experiments.

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Acknowledgements

The authors would like to thank the editor and anonymous reviewers for their helpful comments and suggestions which lead to a considerably improved presentation.

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  1. College of Mathematics and System Sciences, Xinjiang University, Urumqi, 830017, People’s Republic of China

    Shuaijun Liu, Pengzhan Huang & Yinnian He

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  1. Shuaijun Liu
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  2. Pengzhan Huang
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Correspondence to Pengzhan Huang.

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Communicated by: Gianluigi Rozza

This work is supported by the Natural Science Foundation of Xinjiang Uygur Autonomous Region (grant numbers 2023D14014, 2021D01E11) and the Natural Science Foundation of China (grant numbers 12361077, 12271465).

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Liu, S., Huang, P. & He, Y. A second-order scheme based on blended BDF for the incompressible MHD system. Adv Comput Math 49, 74 (2023). https://doi.org/10.1007/s10444-023-10073-9

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