A Mixed Finite Element Method for Stationary Magneto-Heat Coupling System with Variable Coefficients
In this article, a mixed finite element method for thermally coupled, stationary incompressible MHD problems with physical parameters dependent on temperature in the Lipschitz domain is considered. Due to the variable coefficients of the MHD model, the nonlinearity of the system is increased. A stat...
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MDPI AG
2022-06-01
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| Series: | Entropy |
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| Online Access: | https://www.mdpi.com/1099-4300/24/7/912 |
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| author | Qianqian Ding Xiaonian Long Shipeng Mao |
| author_facet | Qianqian Ding Xiaonian Long Shipeng Mao |
| author_sort | Qianqian Ding |
| collection | DOAJ |
| description | In this article, a mixed finite element method for thermally coupled, stationary incompressible MHD problems with physical parameters dependent on temperature in the Lipschitz domain is considered. Due to the variable coefficients of the MHD model, the nonlinearity of the system is increased. A stationary discrete scheme based on the coefficients dependent temperature is proposed, in which the magnetic equation is approximated by Nédélec edge elements, and the thermal and Navier–Stokes equations are approximated by the mixed finite elements. We rigorously establish the optimal error estimates for velocity, pressure, temperature, magnetic induction and Lagrange multiplier with the hypothesis of a low regularity for the exact solution. Finally, a numerical experiment is provided to illustrate the performance and convergence rates of our numerical scheme. |
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| format | Article |
| id | doaj.art-8e666f3062e04c4a80a9fee0e85f5c22 |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-03-09T03:27:30Z |
| publishDate | 2022-06-01 |
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| record_format | Article |
| series | Entropy |
| spelling | doaj.art-8e666f3062e04c4a80a9fee0e85f5c222023-12-03T15:00:15ZengMDPI AGEntropy1099-43002022-06-0124791210.3390/e24070912A Mixed Finite Element Method for Stationary Magneto-Heat Coupling System with Variable CoefficientsQianqian Ding0Xiaonian Long1Shipeng Mao2School of Mathematics, Shandong University, Jinan 250100, ChinaCollege of Mathematics and Information Science, Henan University of Economics and Law, Zhengzhou 450045, ChinaNCMIS, LSEC, Institute of Computational Mathematics and Scientific/Enginnering Computing, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, School of Mathematical Science, University of Chinese Academy of Sciences, Beijing 100190, ChinaIn this article, a mixed finite element method for thermally coupled, stationary incompressible MHD problems with physical parameters dependent on temperature in the Lipschitz domain is considered. Due to the variable coefficients of the MHD model, the nonlinearity of the system is increased. A stationary discrete scheme based on the coefficients dependent temperature is proposed, in which the magnetic equation is approximated by Nédélec edge elements, and the thermal and Navier–Stokes equations are approximated by the mixed finite elements. We rigorously establish the optimal error estimates for velocity, pressure, temperature, magnetic induction and Lagrange multiplier with the hypothesis of a low regularity for the exact solution. Finally, a numerical experiment is provided to illustrate the performance and convergence rates of our numerical scheme.https://www.mdpi.com/1099-4300/24/7/912magnetohydrodynamicsvariable coefficientsmixed element methoduniquenesspartial differential equationsstationary flows |
| spellingShingle | Qianqian Ding Xiaonian Long Shipeng Mao A Mixed Finite Element Method for Stationary Magneto-Heat Coupling System with Variable Coefficients Entropy magnetohydrodynamics variable coefficients mixed element method uniqueness partial differential equations stationary flows |
| title | A Mixed Finite Element Method for Stationary Magneto-Heat Coupling System with Variable Coefficients |
| title_full | A Mixed Finite Element Method for Stationary Magneto-Heat Coupling System with Variable Coefficients |
| title_fullStr | A Mixed Finite Element Method for Stationary Magneto-Heat Coupling System with Variable Coefficients |
| title_full_unstemmed | A Mixed Finite Element Method for Stationary Magneto-Heat Coupling System with Variable Coefficients |
| title_short | A Mixed Finite Element Method for Stationary Magneto-Heat Coupling System with Variable Coefficients |
| title_sort | mixed finite element method for stationary magneto heat coupling system with variable coefficients |
| topic | magnetohydrodynamics variable coefficients mixed element method uniqueness partial differential equations stationary flows |
| url | https://www.mdpi.com/1099-4300/24/7/912 |
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