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

作　　者：DONG Xiao Jing HE Yin Nian 

机构地区：[1]School of Mathematics and Statistics, Xi'an Jiaotong University

出　　处：《Science China Mathematics》2016年第3期589-608,共20页中国科学：数学（英文版）

基　　金：National Natural Science Foundation of China (Grant Nos. 11271298 and 11362021)

摘　　要：Based on the 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.Based on the 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.

关 键 词：stationary incompressible magnetohydrodynamics finite element method iterative method twolevel algorithms 

分 类 号：O357.1[理学—流体力学]