A least-squares non-polynomial finite element method for solving the polygonal-line grating problem

This paper is concerned with the diffraction by a polygonal-line grating. Using the Fourier–Bessel functions that capture the singularities at corners, and representing the diffraction field towards infinity by a truncation of the Rayleigh expansion, we propose a least-squares finite element method for solving the problem. We analyze the convergence and give an error estimate for the method. Numerical experiments are also presented to show the effectiveness of our method.