A $T-ψ$ Finite Element Method for a Nonlinear Degenerate Eddy Current Model with Ferromagnetic Materials

Abstract

This paper is devoted to the study of a fully discrete $T-\psi$ 8finite element method based on $H$-decomposition to solve a nonlinear degenerate transient eddy current problem with ferromagnetic materials. Here, the ferromagnetic properties are linked by a power material law. We first design a nonlinear time-discrete scheme for approximation in suitable function spaces. We show the well-posedness of the semidiscrete problem and prove the convergence of the nonlinear scheme by the Minty-Browder technique. Finally, we suggest a fully discrete scheme, derive its error estimate and give some numerical experiments to validate the theoretical result.