An Adaptive Finite Element Method with a Modified Perfectly Matched Layer Formulation for Diffraction Gratings (Communications in Computational Physics, 2018)
For numerical simulation of one-dimensional diffraction gratings both in TEand TM polarization, an enhanced adaptive finite element method is proposed in thispaper. A modified perfectly matched layer (PML) formulation is proposed for the truncationof the unbounded domain, which results in a homogeneous Dirichlet boundarycondition and the corresponding error estimate is greatly simplified. The a posteriorierror estimates for the adaptive finite element method are provided. Moreover, a lowerbound is obtained to demonstrate that the error estimates obtained are sharp.