Stability and convergence of iterative finite element methods for the thermally coupled incompressible MHD flow

Abstract

Purpose

The purpose of this paper is to propose three iterative finite element methods for equations of thermally coupled incompressible magneto-hydrodynamics (MHD) on 2D/3D bounded domain. The detailed theoretical analysis and some numerical results are presented. The main results show that the Stokes iterative method has the strictest restrictions on the physical parameters, and the Newton’s iterative method has the higher accuracy and the Oseen iterative method is stable unconditionally.

Design/methodology/approach

Three iterative finite element methods have been designed for the thermally coupled incompressible MHD flow on 2D/3D bounded domain. The Oseen iterative scheme includes solving a linearized steady MHD and Oseen equations; unconditional stability and optimal error estimates of numerical approximations at each iterative step are established under the uniqueness condition. Stability and convergence of numerical solutions in Newton and Stokes’ iterative schemes are also analyzed under some strong uniqueness conditions.

Findings

This work was supported by the NSF of China (No. 11971152).

Originality/value

This paper presents the best choice for solving the steady thermally coupled MHD equations with different physical parameters.

Citation

Yang, J. and Zhang, T. (2020), "Stability and convergence of iterative finite element methods for the thermally coupled incompressible MHD flow", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 30 No. 12, pp. 5103-5141. https://doi.org/10.1108/HFF-11-2019-0821