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Abstract
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.
Acknowledgements
The author would like to express her sincere gratitude to her supervisors Professor Jun Zou and Professor Zhouping Xin for their guidance and constant encouragement during her PhD studies. The author also thanks Professor Yinbin Deng for his useful suggestions. Research supported in part by the NSFC.