The simulation of nonlinear magneto-heat coupling model approached by finite element method

Abstract This article is devoted to the exploration of finite element methodfor magneto-heat coupling model, where the eddy current problem and the heat equation are coupled together with the heat convection and the radiation effects. The main contribution is consist of three parts. Firstly, the decoupled scheme is established by applying backward Euler discretization in time and Nédélec-Lagrange finite element in magnetic-temperature field, respectively. Secondly, the existence uniqueness and stability of the numerical solutions are proved by applying the theory of monotoneoperators. Thirdly, the error estimate with the convergent order $O(\tau+h^{\min\{ r,1\}}), \frac{1}{2} < r ≤ 1 under a lower regular assumption. Eventually, two numerical examples are provided. 2008 MSC: 65M60, 65M15, 35Q60, 35B45.