Abstract
In this paper, a fully decoupled finite element algorithm with second order time-accuracy is proposed for the incompressible magnetohydrodynamic(MHD) equations. The algorithm is designed by introducing a nonlocal scalar variable, and combining second order backward differential formula(BDF2), pressure-correction method and fully explicit treatment for the nonlinear terms for temporal discretization with mixed finite element methods for spatial discretization. Furthermore, the unique solvability and unconditional stability of the algorithm are proved. Finally, numerical experiments are performed to verify the efficiency and accuracy of the proposed algorithm.
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