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Finite element approximation of time harmonic waves in periodic structures. (English) Zbl 0853.65134

The diffraction of a time-harmonic electromagnetic plane wave incident on a periodic surface of some inhomogeneous material is considered. The model is reduced to a boundary value problem for the two-dimensional Helmholtz equation which is treated by the finite element method. Some error estimates are established.

MSC:

65Z05 Applications to the sciences
78A45 Diffraction, scattering
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
35Q60 PDEs in connection with optics and electromagnetic theory
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
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