Error Analysis of BDF-Galerkin FEMs for Thermally Coupled Incompressible MHD with Temperature Dependent Parameters (East Asian Journal on Applied Mathematics, 2024)
In this paper, we consider the electromagnetically and thermally driven flowwhich is modeled by evolutionary magnetohydrodynamic equations and heat equationcoupled through generalized Boussinesq approximation with temperature-dependentcoefficients. 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 thetemporal-spatial error splitting technique. Numerical examples are presented to checkthe accuracy and efficiency of the scheme.
Keywords: Thermally coupled magnetohydrodynamic; Boussinesq approximation; temperature dependent coefficient; linearized BDF scheme; convergence.