Error estimation of electromagnetic properties in periodic composite materials

Abstract

This paper addresses the a priori error estimation of the homogenized constitutive parameters (HCPs), the macroscopic field and the limit electromagnetic field in 3D periodic structure. The HCPs and the macroscopic field are approximated respectively by using the Lagrange and the first order Nédélec conforming finite element method. The approximation of limit field is derived from those of HCPs and macroscopic field. The optimality of the convergence is obtained for these electromagnetic quantities and the theoretical results of this work are reinforced by some numerical ones.