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

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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 L2-norm are derived. Meanwhile, the numerical investigations provide a sufficient support for the theoretical analysis.

Keywords

MHD equations
Semi-implicit scheme
Crank–Nicolson extrapolation scheme
Stability and convergence
Finite element method

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