A finite-element approximation of a quasi-magnetostatic 3D eddy current model by fractional-step A-ψ scheme

We propose in this paper a fractional-step A-ψ scheme for a quasi-magnetostatic 3D eddy current model by means of finite-element approximations. Bounds for continuous and discrete error in finite time are given, and it is verified that provided the time step τ is sufficiently small, the proposed algorithm yields for finite time T an error of O(h2+τ2 in the L2-norm for the magnetic field H(= v∇ × A), where h is the mesh size.