A Posteriori Error Analysis of the PML Finite Volume Method for the Scattering Problem by a Periodic Chiral Structure

Abstract

In this paper, we consider the electromagnetic wave scattering problem from a periodic chiral structure. The scattering problem is simplified to a two-dimensional problem, and is discretized by a finite volume method combined with the perfectly matched layer (PML) technique. A residual-type a posteriori error estimate of the PML finite volume method is analyzed and the upper and lower bounds on the error are established in the $H^1$-norm. The crucial part of the a posteriori error analysis is to derive the error representation formula and use a $L^2$-orthogonality property of the residual which plays a similar role as the Galerkin orthogonality. An adaptive PML finite volume method is proposed to solve the scattering problem. The PML parameters such as the thickness of the layer and the medium property are determined through sharp a posteriori error estimate. Finally, numerical experiments are presented to illustrate the efficiency of the proposed method.