Adaptive Fourier finite element method for three-dimensional time-harmonic Maxwell's equations in axisymmetric domains

The aim of this paper is to consider adaptive method for the time-harmonic Maxwell equations and their Perfectly Matched Layer (PML) equations in three-dimensional (3D) axisymmetric domains. The adaptive method is based on Fourier decomposition which reduces the 3D problems into a sequence of two-dimensional (2D) problems and each Fourier coefficient satisfies a system of equations on the meridian domain. A recovery type a posterior error estimator is proposed as the error estimator for time-harmonic Maxwell's equations. Numerical examples are presented to indicate the efficiency of the proposed error estimator and the corresponding adaptive method.