An iterative scheme for a geodynamo system

In this paper we propose an iterative scheme for a nonlinear spherical geodynamo model and carry out convergence analysis of this scheme. Our model is a coupled system of fluid velocity u , total kinematic pressure P and magnetic field B . They are governed by the Navier–Stokes equations and the dynamo equations. Using the mathematical induction method and energy estimates, it is concluded that our iterative scheme converges in the L ^∞(0, T; H ¹) sense and in the L ²(0, T; H ²) sense.