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Error estimates of H(div)-conforming method for nonstationary magnetohydrodynamic system

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Abstract

In this paper, we focus on pressure-robust analysis of a mixed finite element method for the numerical discretization of nonstationary magnetohydrodynamics system. The velocity field is discretized by divergence-conforming Raviart-Thomas spaces with interior penalties, and the magnetic equation is approximated by curl-conforming Nédélec edge elements. The main feature of the method is that it produces exactly divergence-free velocity approximation, and captures the strongest magnetic singularities. The results show that the proposed scheme meets a discrete unconditional energy stability and the numerical solution is well-posedness. In addition, a priori error estimates are given, in which the constants are independent of the Reynolds number. Finally, we provide several numerical results illustrating the good performance of the scheme and confirming the theoretical rates of convergence.

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Acknowledgements

The authors thank the anonymous referees very much for their valuable comments and suggestions which helped to improve the quality of this paper.

Funding

This work is supported by the Natural Science Foundation of China (Nos. 11871467 and 12161141017), Shandong Province Natural Science Foundation (ZR2021QA054) and China Postdoctoral Science Foundation (2021M691951).

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Authors and Affiliations

  1. School of Mathematics, Shandong University, Jinan, 250100, China

    Qianqian Ding

  2. NCMIS, LSEC, Institute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, School of Mathematical Science, University of Chinese Academy of Sciences, Beijing, 100190, China

    Shipeng Mao & Jiaao Sun

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  1. Qianqian Ding
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  2. Shipeng Mao
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Correspondence to Shipeng Mao.

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Ding, Q., Mao, S. & Sun, J. Error estimates of H(div)-conforming method for nonstationary magnetohydrodynamic system. Adv Comput Math 48, 55 (2022). https://doi.org/10.1007/s10444-022-09964-0

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