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This paper is devoted to the study of a fully discrete T-ψ finite 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. [ABSTRACT FROM AUTHOR]

Fully discrete potential-based finite element methods called $${\mathbf{A}-\phi}$$ methods are used to solve a transient eddy current problem in a three-dimensional convex bounded polyhedron. Using $${\mathbf{A}-\phi}$$ methods, fully discrete coupled and decoupled numerical schemes are developed. The existence and uniqueness of solutions for these schemes together with the energy-norm error estimates are provided. To verify the validity of both schemes, some computer simulations are performed for the model from TEAM Workshop Problem 7. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the finite element A -- ø method to approximate the eddy current equations with discontinuous coefficients in general three-dimensional Lipschitz polyhedral eddy current region. Nonmatching finite element meshes on the interface are considered and optimal error estimates are obtained. [ABSTRACT FROM AUTHOR]