Fully discrete T‐ψ finite element method to solve a nonlinear induction hardening problem

Abstract

We study an induction hardening model described by Maxwell's equations coupled with a heat equation. The magnetic induction field is assumed a nonlinear constitutional relation and the electric conductivity is temperature-dependent. The Tmethod is to transform Maxwell's equations to the vector-scalar potential formulations and to solve the potentials by means of the finite element method. In this article, we present a fully discrete Tfinite element scheme for this nonlinear coupled problem and discuss its solvability. We prove that the discrete solution converges to a weak solution of the continuous problem. Finally, we conclude with two numerical experiments for the coupled system.