Finite Element Analysis for Nonstationary Magneto-Heat Coupling Problem

Abstract

This paper is devoted to finite element analysis for the magneto-heat coupling model which governs the electromagnetic fields in large power transformers. The model, which couples Maxwell's equations and Heat equation through Ohmic heat source, is nonlinear. First we derive an equivalent weak formulation for the nonlinear magneto-heat model. We propose a linearized and temporally discrete scheme to approximate the continuous problem. The well-posedness and error estimates are proven for the semi-discrete scheme. Based on the results, we propose a fully discrete finite element problem and prove the error estimates for the approximate solutions. To validate the magneto-heat model and verify the efficiency of the finite element method, we compute an engineering benchmark problem of the International Compumag Society, P21^b-MN. The numerical results agree well with experimental data.