A Posteriori Error Analysis of the PML Finite Volume Method for the Scattering Problem by a Periodic Chiral Structure (Journal of Computational Mathematics, 2024)
In this paper, we consider the electromagnetic wave scattering problem from a periodicchiral structure. The scattering problem is simplified to a two-dimensional problem, and isdiscretized 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 methodis 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 representationformula and use a $L^2$-orthogonality property of the residual which plays a similar roleas the Galerkin orthogonality. An adaptive PML finite volume method is proposed tosolve the scattering problem. The PML parameters such as the thickness of the layer andthe medium property are determined through sharp a posteriori error estimate. Finally,numerical experiments are presented to illustrate the efficiency of the proposed method.
Keywords: Finite volume method; Perfectly matched layer; A posteriori error analysis; Chiral media.