Optimal convergence analysis of Crank-Nicolson extrapolation scheme for the three-dimensional incompressible magnetohydrodynamics

Abstract This paper considers a Crank–Nicolson extrapolation scheme based on mixed finite element method to solve the three-dimensional incompressible magnetohydrodynamics (MHD) equations. We prove that the fully discrete scheme is almost unconditionally stable and convergent, i.e., stable and convergent when the time step is less than or equal to a constant. By a new negative norm technique, the optimal error estimates in L 2 -norm are derived. Meanwhile, the numerical investigations provide a sufficient support for the theoretical analysis.

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