Finite element analysis of an A–ϕ method for time-dependent Maxwell’s equations based on explicit-magnetic-field scheme

In this paper, error analysis of a finite element A–ϕ method for the time-dependent Maxwell’s equations is presented. An explicit-magnetic-field scheme is applied. Provided that the time-stepsize τ is sufficiently small, the proposed algorithm yields for finite time T   an error of O(τ2+τ-1h4+h2) in the L2-norm for the electric field E and the magnetic field H, where h is the mesh size.