A Least-Squares Finite Element Analysis for Diffraction Problems

Abstract

The diffraction of a time harmonic wave incident upon a grating (or periodic) structure is treated by a least-squares finite element method that incorporates the jump conditions at interfaces into the objective functional. Two fundamental polarizations are considered. Coercivity of the quadratic functional is established and optimal discretization error estimates are obtained in both cases. The theoretical results indicate that, for sufficiently smooth interfaces, the error estimates are superior to those of standard finite element methods.