Abstract
In this paper, we propose an error analysis of fully decoupled time-discrete scheme for the Cahn–Hilliard-MHD (CHMHD) diffuse interface model. Firstly, we use the “zero-energy-contribution" technique to reconstruct the system by introducing three scalar auxiliary variables (SAV). Secondly, we construct first-order semi-discrete SAV scheme for this new system by using pressure-correction method, and we also demonstrate its unconditional stability in energy. Then, we give a detailed implementation procedure to show that the proposed scheme is linear and fully decoupled, and only a series of elliptic equations with constant coefficients need to be solved at each time step. Moreover, we establish the optimal convergence rate by rigorous error analysis. Finally, we present numerical experiments to validate the accuracy, stability and efficiency of the proposed scheme.
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Data Availability Statement
The data that support the findings of this study are available from the corresponding author upon reasonable request.
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Acknowledgements
This work was supported by the Research Project Supported by Shanxi Scholarship Council of China (No.2021-029), International Cooperation Base and Platform Project of Shanxi Provincial (202104041101019), Basic Research Plan of Shanxi Province (202203021211129), Shanxi Province Natural Science Research (No. 202203021212249) and Special/Youth Foundation of Taiyuan University of Technology (No. 2022QN101).
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Wang, D., Wang, Z., Zhang, C. et al. Error analysis of fully decoupled SAV scheme for two phase magnetohydrodynamic diffuse interface model. Comp. Appl. Math. 43, 374 (2024). https://doi.org/10.1007/s40314-024-02891-4
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DOI: https://doi.org/10.1007/s40314-024-02891-4