Convergence of A-ϕ ⊕ A scheme for 3D eddy current model based on ungauged electromagnetic potentials

The A-ϕ ⊕ A schemes for 3D eddy current model based on ungauged potentials are presented. The finite element error estimates of this method in finite time T are given. And it is verified that provided the time-stepsize τ is sufficiently small, the proposed algorithm yields for finite time T an error of O(τ2+h2) on coupled A-ϕ ⊕ A scheme in the L2-norm for the electric field E in the eddy-current domain Ω1 and the magnetic field H in the whole domain Ω, and of O(τ+τ-1h4+h2) on two decoupled A-ϕ ⊕ A scheme for the electric field E in the eddy-current domain Ω1 and the magnetic field H in the whole domain Ω, where h is the mesh size.