Finite-element method for time-dependent Maxwellʹs equations based on an explicit-magnetic-field scheme

This paper provides a convergence analysis of the finite-element method for time-dependent Maxwellʹs equations by means of an explicit-magnetic-field scheme. Error estimates in finite time 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 ( h s + τ ) in the L 2 -norm for the electric field E , the magnetic field H , where h is the mesh size and 1 2 < s ⩽ 1 . In addition, some numerical results are reported in the paper.