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Keywords:
magnetohydrodynamic equation; two-grid method; penalty method; Arrow-Hurwicz method; stability; error estimation
magnetohydrodynamic equation; two-grid method; penalty method; Arrow-Hurwicz method; stability; error estimation
Summary:
We propose and analyze three kinds of two-grid penalty Arrow-Hurwicz (A-H) iterative finite element methods for the stationary incompressible magnetohydrodynamic (MHD) equations, which adopt the existing A-H iterative method to obtain the coarse mesh solution, and then correct the solution by three different one-step schemes (Oseen type, Stokes type and Newton type) with the usual penalty method on the fine mesh. These methods combine the A-H iterative method, the penalty method and the two-grid strategy, maintaining the advantage of three methods and overcoming some of their limitations. Rigorous analysis of the optimal error estimate and stability for three methods are provided. Ample numerical experiments are reported to validate the theoretical results and the efficiency of the numerical schemes.
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