TY - JOUR
T1 - A Posteriori Error Analysis of the PML Finite Volume Method for the Scattering Problem by a Periodic Chiral Structure
AU - Wang , Zhoufeng
AU - Liu , Muhua
JO - Journal of Computational Mathematics
VL - 2
SP - 413
EP - 437
PY - 2024
DA - 2024/11
SN - 43
DO - http://doi.org/10.4208/jcm.2305-m2022-0234
UR - https://global-sci.org/intro/article_detail/jcm/23544.html
KW - Finite volume method, Perfectly matched layer, A posteriori error analysis,
Chiral media.
AB - <p style="text-align: justify;">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.</p>