Error estimate of a first-order time discretization scheme for the geodynamo equations

In this paper, we analyze a first-order time discretization scheme for a nonlinear geodynamo model and carry out the convergence analysis of this numerical scheme. It is concluded that our numerical scheme converges with first-order accuracy in the sense of L 2 -norm with respect to the velocity field u and the magnetic field B and with half-order accuracy in time for the total kinematic pressure P.