Fully discrete potential-based finite element methods for a transient eddy current problem

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.