Abstract
In this paper, a second-order backward differentiation formula (BDF) scheme for a hybrid MHD system is considered. Being different with the steady and nonstationary MHD equations, the hybrid MHD system is coupled by the time-dependent Navier-Stokes equations and the steady Maxwell equations. By using the standard extrapolation technique for the nonlinear terms, the proposed BDF scheme is a semi-implicit scheme. Furthermore, this scheme is a decoupled scheme such that the magnetic field and the velocity can be solved independently at the same time as discrete level. A rigorous error analysis is done and we prove the unconditionally optimal second-order convergence rate \(\mathcal O(h^{2}+({\Delta } t)^{2})\) in L2 norm for approximations of the magnetic field and the velocity, where h and Δt are the grid mesh and the time step, respectively. Finally, the numerical results are displayed to illustrate the theoretical results.
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Funding
This work was supported by National Natural Science Foundation of China (No.11771337) and by Zhejiang Provincial Natural Science Foundation (No. LY18A010021).
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Communicated by: Jan Hesthaven
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Li, Y., Zhai, C. Unconditionally optimal convergence analysis of second-order BDF Galerkin finite element scheme for a hybrid MHD system. Adv Comput Math 46, 75 (2020). https://doi.org/10.1007/s10444-020-09815-w
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DOI: https://doi.org/10.1007/s10444-020-09815-w