A space-time discretization for an electromagnetic problem with moving non-magnetic conductor

Abstract

This paper deals with a space-time discretization scheme for an eddy current problem in a multi-component domain with a moving non-magnetic conductor. We incorporate the Coulomb gauge to the formulation, then propose a fully-discrete finite element scheme combined with backward Euler's method to find an approximation of the solution to the variational system. The convergence of the scheme is proved, and the error estimates for the first-order Lagrangian finite elements are established. Under appropriate assumptions on the weak solution and the given initial data, we show the optimal convergence rate for the space discretization and the suboptimal rate for time discretization. Some numerical experiments are performed to support the obtained theoretical results.