Abstract
In this paper, we study efficient schemes and design robust preconditioners for solving incompressible MHD (magnetohydrodynamics) system. We propose the first order and second order symmetric schemes with augmented terms in magnetic equations that are introduced in consideration of designing uniformly robust preconditioners. We present optimal error estimates of the proposed time-matching scheme. Further, we design block diagonal preconditioners for the schemes, and rigorously prove that the condition number of preconditioned system is uniformly bounded by a constant which only depends on the domain Ω. Finally, some numerical experiments, including accuracy tests and physical benchmark problems, are presented to verify the accuracy of the schemes and the robustness of the preconditioner.
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