Abstract
In the paper we consider the one-level and two-level iterative penalty finite element methods for the steady incompressible magnetohydrodynamic problem based on the iteration of pressure with a factor of penalty parameter. Firstly, the \(\mathbf {H}^1\) and \(\mathbf {L}^2\) error estimates of numerical solutions of one-level iterative penalty finite element method are provided. Secondly, the stability and convergence of two-level iterative penalty finite element method are analyzed. Finally, some numerical results are provided to verify the effectiveness of the developed numerical schemes.
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Communicated by Jorge X. Velasco.
This work was supported by CAPES and CNPq, Brazil (No. 88881.068004/2014.01), the NSF of China (No. 11301157), the Doctor Fund of Henan Polytechnic University (B2012-098) and the Foundation of Distinguished Young Scientists of Henan Polytechnic University (J2015-05).
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Deng, J., Tao, Z. & Zhang, T. Iterative penalty finite element methods for the steady incompressible magnetohydrodynamic problem. Comp. Appl. Math. 36, 1637–1657 (2017). https://doi.org/10.1007/s40314-016-0323-y
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DOI: https://doi.org/10.1007/s40314-016-0323-y