Error Analysis of BDF-Galerkin FEMs for Thermally Coupled Incompressible MHD with Temperature Dependent Parameters
Year: 2024
Author: Shuaijun Liu, Pengzhan Huang, Yinnian He
East Asian Journal on Applied Mathematics, Vol. 14 (2024), Iss. 4 : pp. 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 L2-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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/eajam.2023-085.070723
East Asian Journal on Applied Mathematics, Vol. 14 (2024), Iss. 4 : pp. 731–768
Published online: 2024-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 38
Keywords: Thermally coupled magnetohydrodynamic Boussinesq approximation temperature dependent coefficient linearized BDF scheme convergence.