A Modular Grad-Div Stabilization for the 2D/3D Nonstationary Incompressible Magnetohydrodynamic Equations

In this paper, we study an efficient and modular grad-div stabilization algorithm for the 2D/3D nonstationary incompressible magnetohydrodynamic equations. The considered algorithm is a fully discrete first-order scheme based on the mixed finite element method and does not increase computational time for increasing stabilization parameters. Also, both unconditional stability and convergence analysis are given. Finally, numerical experiments are presented to verify both the numerical theory and efficiency of the presented algorithm.

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