Convergence analysis of a temporally second-order accurate finite element scheme for the Cahn-Hilliard-Magnetohydrodynamics system of equations

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 L & INFIN;& tau;(0, T; H1) norm, and for the velocity and the magnetic fields in the L & INFIN;& tau;(0, T; L2) norm, respectively. Numerical examples are presented to validate the theoretical results of the proposed scheme.& COPY; 2023 Elsevier B.V. All rights reserved.