Error correction iterative finite element method based on charge-conservative for the stationary inductionless magnetohydrodynamic system
Yande Xia
Department of Mathematics, Yunnan Normal University, Kunming, PR China
Search for more papers by this authorCorresponding Author
Yun-Bo Yang
Department of Mathematics, Yunnan Normal University, Kunming, PR China
Yunnan Key Laboratory of Model Analytical Mathematics and Application, Yunnan Normal University, Kunming, PR China
Key Laboratory of Complex System Modeling and Application for Universities in Yunnan, Yunnan Normal University, Kunming, PR China
Correspondence
Yun-Bo Yang, Department of Mathematics, Yunnan Normal University, Kunming, 650500, PR China.
Email: [email protected]
Search for more papers by this authorYande Xia
Department of Mathematics, Yunnan Normal University, Kunming, PR China
Search for more papers by this authorCorresponding Author
Yun-Bo Yang
Department of Mathematics, Yunnan Normal University, Kunming, PR China
Yunnan Key Laboratory of Model Analytical Mathematics and Application, Yunnan Normal University, Kunming, PR China
Key Laboratory of Complex System Modeling and Application for Universities in Yunnan, Yunnan Normal University, Kunming, PR China
Correspondence
Yun-Bo Yang, Department of Mathematics, Yunnan Normal University, Kunming, 650500, PR China.
Email: [email protected]
Search for more papers by this authorAbstract
In this paper, we propose and analyze a new error correction iterative finite element method (FEM) based on charge-conservative for solving the stationary inductionless magnetohydrodynamic (MHD). The method consists of first solving the inductionless MHD equations by the Oseen iterative scheme to obtain an approximate solution, and then an error correction strategy is applied to control the error arising from the linearization of the nonlinear inductionless MHD equations. The proposed method not only retains the advantages of the classical Oseen iterative scheme but also leads to a rapid rate of convergence. It is shown that the convergence rate of the new method is greatly improved under the uniqueness condition. Stability analysis and error estimates are provided. Numerical results are presented to verify the applicability and effectiveness of the new method.
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