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A partitioned finite element scheme based on Gauge-Uzawa method for time-dependent MHD equations

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Abstract

In this paper, we mainly introduce a partitioned scheme based on Gauge-Uzawa finite element method for the 2D time-dependent incompressible magnetohydrodynamics (MHD) equations. It is a fully decoupled projection method which combines the Gauge and Uzawa methods within a variational formulation. Firstly, the temporal discretization is based on backward Euler technique for the linear term and semi-implicit scheme for the nonlinear term. Secondly, the spatial approximation of fluid velocity, hydrodynamic pressure, and magnetic field apply the mixed element method. Finally, the validity, reliability, and accuracy of the proposed algorithms are supported by numerical experiments.

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Acknowledgments

The authors would like to thank the editor and referees for their valuable comments and suggestions which helped us to improve the results of this paper.

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Authors and Affiliations

  1. College of Mathematics and System Sciences, Xinjiang University, Urumqi, 830046, People’s Republic of China

    Qing Zhang, Haiyan Su & Xinlong Feng

Authors
  1. Qing Zhang
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  2. Haiyan Su
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  3. Xinlong Feng
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Corresponding author

Correspondence to Haiyan Su.

Additional information

This work is in part supported by the NSF of China (No. 11671345 and No. 11362021) and the NSF of Xinjiang Province (No. 2016D01C058)

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Zhang, Q., Su, H. & Feng, X. A partitioned finite element scheme based on Gauge-Uzawa method for time-dependent MHD equations. Numer Algor 78, 277–295 (2018). https://doi.org/10.1007/s11075-017-0376-z

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  • DOI: https://doi.org/10.1007/s11075-017-0376-z

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