In this paper, we develop a adaptive finite volume method with the truncation of the nonlocal boundary operators for the wave scattering by periodic structures. The related truncation parameters are chosen through sharp a posteriori error estimate of the finite volume method. The crucial part of the a posteriori error analysis is to develop a duality argument technique and use a L²-orthogonality property of the residual which plays a similar role as the Galerkin orthogonality. The a posteriori error estimate consists of two parts, the finite volume discretization error for adapting meshes and the truncation error of boundary operators which decays exponentially with respect to the truncation parameter N. Numerical experiments are presented to confirm our theoretical analysis and show the efficiency and robustness of the proposed adaptive method.

在本文中，我们开发了一种自适应有限体积方法，其中截断了周期性结构的波散射的非局部边界算子。相关截断参数是通过有限体积法的尖锐后验误差估计来选择的。后验误差分析的关键部分是开发对偶论证技术并使用残差的L ² -正交性质，其作用与 Galerkin 正交性相似。后验误差估计由两部分组成，用于适应网格的有限体积离散化误差和边界算子的截断误差，它相对于截断参数N呈指数衰减. 数值实验证实了我们的理论分析，并展示了所提出的自适应方法的效率和鲁棒性。