Optimal convergence analysis for a FEM approximation of a transient eddy current problem incorporating velocity terms

This paper aims to study a numerical method to solve a transient eddy current problem involving velocity terms in a bounded domain including conductor and insulator regions. For this purpose, we show that the formulation admits a well-posed saddle point structure given by the curl-free condition for the magnetic field in the insulator domain. We propose a full discretization based on a backward Euler method in time variable and finite element method in space variable. Then, we use Nédélec edge element on the tetrahedral meshes, for which we obtain error estimates. For numerical purposes we used a block-Krylov method to solve the linear system of equations obtained in the fully discretization. Finally, we present some numerical results to validate the theoretical findings obtained.