Abstract
This work is concerned with the study of two-level penalty finite element method for the 2D/3D stationary incompressible magnetohydrodynamics equations. The new method is an interesting combination of the Newton iteration and two-level penalty finite element algorithm with two different finite element pairs \(P_{1}b\)-\(P_{1}\)-\(P_{1}b\) and \(P_{1}\)-\(P_{0}\)-\(P_{1}\). Moreover, the rigorous analysis of stability and error estimate for the proposed method are given. Numerical results verify the theoretical results and show the applicability and effectiveness of the presented scheme.
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The authors sincerely thank the editor and referees for their valuable comments and suggestions which helped us to improve the results of this paper.
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This work is supported by the Natural Science Foundation of Xinjiang Province (No. 2016D01C073).
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Su, H., Feng, X. & Zhao, J. Two-Level Penalty Newton Iterative Method for the 2D/3D Stationary Incompressible Magnetohydrodynamics Equations. J Sci Comput 70, 1144–1179 (2017). https://doi.org/10.1007/s10915-016-0276-8
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DOI: https://doi.org/10.1007/s10915-016-0276-8
Keywords
- Magnetohydrodynamics equations
- Penalty finite element method
- Newton iteration
- Two-level method
- Inf-sup condition
- Error estimate