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Volume 14, Issue 4
Error Analysis of BDF-Galerkin FEMs for Thermally Coupled Incompressible MHD with Temperature Dependent Parameters

Shuaijun Liu, Pengzhan Huang & Yinnian He

East Asian J. Appl. Math., 14 (2024), pp. 731-768.

Published online: 2024-09

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  • Abstract

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.

  • AMS Subject Headings

65M12, 65M60

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COPYRIGHT: © Global Science Press

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@Article{EAJAM-14-731, author = {Liu , ShuaijunHuang , Pengzhan and He , Yinnian}, title = {Error Analysis of BDF-Galerkin FEMs for Thermally Coupled Incompressible MHD with Temperature Dependent Parameters}, journal = {East Asian Journal on Applied Mathematics}, year = {2024}, volume = {14}, number = {4}, pages = {731--768}, abstract = {

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} }
TY - JOUR T1 - Error Analysis of BDF-Galerkin FEMs for Thermally Coupled Incompressible MHD with Temperature Dependent Parameters AU - Liu , Shuaijun AU - Huang , Pengzhan AU - He , Yinnian JO - East Asian Journal on Applied Mathematics VL - 4 SP - 731 EP - 768 PY - 2024 DA - 2024/09 SN - 14 DO - http://doi.org/10.4208/eajam.2023-085.070723 UR - https://global-sci.org/intro/article_detail/eajam/23436.html KW - Thermally coupled magnetohydrodynamic, Boussinesq approximation, temperature dependent coefficient, linearized BDF scheme, convergence. AB -

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.

Liu , ShuaijunHuang , Pengzhan and He , Yinnian. (2024). Error Analysis of BDF-Galerkin FEMs for Thermally Coupled Incompressible MHD with Temperature Dependent Parameters. East Asian Journal on Applied Mathematics. 14 (4). 731-768. doi:10.4208/eajam.2023-085.070723
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