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Convergence of some finite element iterative methods related to different Reynolds numbers for the 2D/3D stationary incompressible magnetohydrodynamics

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Abstract

Based on finite element method (FEM), some iterative methods related to different Reynolds numbers are designed and analyzed for solving the 2D/3D stationary incompressible magnetohydrodynamics (MHD) numerically. Two-level finite element iterative methods, consisting of the classical m-iteration methods on a coarse grid and corrections on a fine grid, are designed to solve the system at low Reynolds numbers under the strong uniqueness condition. One-level Oseen-type iterative method is investigated on a fine mesh at high Reynolds numbers under the weak uniqueness condition. Furthermore, the uniform stability and convergence of these methods with respect to equation parameters R e ,R m , S c , mesh sizes h,H and iterative step m are provided. Finally, the efficiency of the proposed methods is confirmed by numerical investigations.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an, 710049, China

    XiaoJing Dong & YinNian He

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  1. XiaoJing Dong
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  2. YinNian He
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Correspondence to YinNian He.

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Dong, X., He, Y. Convergence of some finite element iterative methods related to different Reynolds numbers for the 2D/3D stationary incompressible magnetohydrodynamics. Sci. China Math. 59, 589–608 (2016). https://doi.org/10.1007/s11425-015-5087-0

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