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Well-Posedness and Finite Element Approximation for the Stationary Magneto-Hydrodynamics Problem with Temperature-Dependent Parameters

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Abstract

In this article we study a well-posedness and finite element approximation for the non-isothermal incompressible magneto-hydrodynamics flow subject to a generalized Boussinesq problem with temperature-dependent parameters. Applying some similar hypotheses in Oyarźua et al. (IMA J Numer Anal 34:1104–1135, 2014), we prove the existence and uniqueness of weak solutions and discrete weak solutions, and derive optimal error estimates for small and smooth solutions. Finally, we provide some numerical results to confirm the rates of convergence.

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Correspondence to Hailong Qiu.

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This work is supported by the Natural Science Foundation of China (11701498, 11801492, 61877052).

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Qiu, H. Well-Posedness and Finite Element Approximation for the Stationary Magneto-Hydrodynamics Problem with Temperature-Dependent Parameters. J Sci Comput 85, 58 (2020). https://doi.org/10.1007/s10915-020-01361-3

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  • DOI: https://doi.org/10.1007/s10915-020-01361-3

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