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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