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 - <p style="text-align: justify;">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.</p>