Convergence of finite element A–ϕ method for solving time-dependent Maxwell’s equations

摘要

This paper provides a convergence analysis of finite element A–ϕ method for the time-dependent Maxwell’s equations based on ungauged potentials. Error estimates 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(h+τ) in the L2-norm for the electric field E and the magnetic field H, where h is the mesh size.