A-θ approaches of an eddy current problem based on solving certain potentials

In this paper, we propose novel finite element A - θ approaches to realize the approximation of a three-dimensional eddy current problem in a bounded domain containing a simply-connected conductor region where the eddy current is formed. These algorithms are based on solving a vector potential in the whole domain by using the edge finite-element method and a local scalar potential only in the conductor region by using the nodal finite-element method. Further, error estimates for coupled and decoupled A - θ schemes are given.