Abstract
In this paper we propose and analyze a temporally second-order accurate numerical scheme for the Cahn–Hilliard-Magnetohydrodynamics system of equations. The scheme is based on a modified Crank–Nicolson-type approximation for the time discretization and a mixed finite element method for the spatial discretization. The modified Crank–Nicolson approximation enables us to carry out the mass conservation and the energy stability analysis. Error estimates are derived for the phase field in the Lτ∞(0,T;H1) norm, and for the velocity and the magnetic fields in the Lτ∞(0,T;L2) norm, respectively. Numerical examples are presented to validate the theoretical results of the proposed scheme.
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