Electric potential-robust iterative analysis of charge-conservative conforming FEM for thermally coupled inductionless MHD system

Abstract

This paper mainly considers electric potential-robust iterative methods based on conservation of charge in Lipschitz domain for the 2D/3D stationary thermally coupled inductionless MHD equations. Based on the hybrid finite element method, the unknowns of hydrodynamic are discretized by the stable velocity–pressure finite element pair, and the current density along with electric potential are similarly discretized by the conforming finite element pair in H(div,Ω)×L2(Ω). It is proved especially that the optimal error estimates of velocity, current density, temperature and pressure do not depend on electric potential. And on account of the strong nonlinearity of the equations, we present three coupled iterative methods, namely, the Stokes, Newton and Oseen iterations and the convergence and stability under different uniqueness conditions are analyzed strictly. The theoretical analysis is validated by the given numerical results, and for the proposed methods, the applicability and effectiveness are demonstrated.