CONVERGENCE ANALYSIS OF SOME FINITE ELEMENT PARALLEL ALGORITHMS FOR THE STATIONARY INCOMPRESSIBLE MHD EQUATIONS  

作　　者：Xiaojing Dong Yinnian He 

机构地区：[1]Hunan Key Laboratory for Computation and Simulation in Science and Engineering,Key Laboratory of Intelligent Computing&Information Processing of Ministry of Education,School of Mathematics and Computational Science,Xiangtan University,Xiangtan 411105,China [2]Institute of Applied Physics and Computational Mathematics,Beijing 100088,China [3]School of Mathematics and Statistics,Xi'an Jiaotong University,Xi'an 710049,China

出　　处：《Journal of Computational Mathematics》2024年第1期49-70,共22页计算数学（英文）

基　　金：supported by the National Natural Science Foundation of China(Grant Nos.12071404,12271465,12026254);by the Young Elite Scientist Sponsorship Program by CAST(Grant No.2020QNRC001);by the China Postdoctoral Science Foundation(Grant No.2018T110073);by the Natural Science Foundation of Hunan Province(Grant No.2019JJ40279);by the Excellent Youth Program of Scientific Research Project of Hunan Provincial Department of Education(Grant No.20B564);by the International Scientific and Technological Innovation Cooperation Base of Hunan Province for Computational Science(Grant No.2018WK4006).

摘　　要：By combination of iteration methods with the partition of unity method(PUM),some finite element parallel algorithms for the stationary incompressible magnetohydrodynamics(MHD)with different physical parameters are presented and analyzed.These algorithms are highly efficient.At first,a global solution is obtained on a coarse grid for all approaches by one of the iteration methods.By parallelized residual schemes,local corrected solutions are calculated on finer meshes with overlapping sub-domains.The subdomains can be achieved flexibly by a class of PUM.The proposed algorithm is proved to be uniformly stable and convergent.Finally,one numerical example is presented to confirm the theoretical findings.

关 键 词：Partition of unity method Local and parallel algorithm Finite element method Iteration methods MAGNETOHYDRODYNAMICS 

分 类 号：O17[理学—数学]