Convergence Analysis of Finite Element Approximation for 3-D Magneto-Heating Coupling Model

Abstract

In this paper, the magneto-heating model is considered, where the nonlinear terms conclude the coupling magnetic diffusivity, the turbulent convection zone, the flow fields, ohmic heat, and α-quench. The highlights of this paper consist of three parts. Firstly, the solvability of the model is derived from Rothe's method and Arzela-Ascoli theorem after setting up the decoupled semi-discrete system. Secondly, the well-posedness for the full-discrete scheme is arrived and the convergence order $O$($h$^min{$s$,$m$}+$τ$) is obtained, respectively, where the approximation scheme is based on backward Euler discretization in time and Nédélec-Lagrangian finite elements in space. At last, a numerical experiment demonstrates the expected convergence.