Convergence analysis of adaptive edge finite element method for variable coefficient time-harmonic Maxwell’s equations

Abstract

In this paper, our main goal is to study the convergence analysis of adaptive edge finite element method (AEFEM) based on arbitrary order Nédélec edge elements for the variable-coefficient time-harmonic Maxwell’s equations, i.e., we prove that the AEFEM gives a contraction for the sum of the energy error and the error estimator, between two consecutive adaptive loops provided the initial mesh is fine enough. First, we give the variational problem of the variable-coefficient time-harmonic Maxwell’s equations and the posteriori error estimator of the residual type. Then we establish the quasi-orthogonality, the global upper bound of the error, the compressibility of the error estimator, and prove the convergence result. Finally, our numerical results verify that the error estimator is valid.