East Asian J. Appl. Math., 14 (2024), pp. 731-768.
Published online: 2024-09
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In this paper, we consider the electromagnetically and thermally driven flow which is modeled by evolutionary magnetohydrodynamic equations and heat equation coupled through generalized Boussinesq approximation with temperature-dependent coefficients. Based on a third-order backward differential formula for temporal discretization, mixed finite element approximation for spatial discretization and extrapolated treatments in linearization for nonlinear terms, a linearized backward differentiation formula type scheme for the considered equations is proposed and analysed. Optimal $L^2$-error estimates for the proposed fully discretized scheme are obtained by the temporal-spatial error splitting technique. Numerical examples are presented to check the accuracy and efficiency of the scheme.
}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.2023-085.070723}, url = {http://global-sci.org/intro/article_detail/eajam/23436.html} }In this paper, we consider the electromagnetically and thermally driven flow which is modeled by evolutionary magnetohydrodynamic equations and heat equation coupled through generalized Boussinesq approximation with temperature-dependent coefficients. Based on a third-order backward differential formula for temporal discretization, mixed finite element approximation for spatial discretization and extrapolated treatments in linearization for nonlinear terms, a linearized backward differentiation formula type scheme for the considered equations is proposed and analysed. Optimal $L^2$-error estimates for the proposed fully discretized scheme are obtained by the temporal-spatial error splitting technique. Numerical examples are presented to check the accuracy and efficiency of the scheme.