Convergence of an Alternating A-$φ$ Scheme for Quasi-Magnetostatics Eddy Current Problem (Journal of Computational Mathematics, 2004)
We propose in this paper an alternating A-$φ$ method for the quasi-magnetostatic eddy current problem 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 $O(h+τ^{1/2})$ in the $L^2$-norm for the magnetic field $H(= μ^{-1} abla × A)$, where $h$ is the mesh size, $μ$ the magnetic permeability.
Keywords: Eddy current problem; Alternating $A-φ$ method; Finite element approximation; Error estimate.