A variant of the plane wave least squares method for the time-harmonic Maxwell’s equations

Abstract

In this paper we are concerned with the plane wave method for the discretization of time-harmonic Maxwell’s equations in three dimensions. As pointed out in Hiptmair et al. (Math. Comput. 82 (2013) 247–268), it is difficult to derive a satisfactory L2 error estimate of the standard plane wave approximation of the time-harmonic Maxwell’s equations. We propose a variant of the plane wave least squares (PWLS) method and show that the new plane wave approximations yield the desired L2 error estimate. Moreover, the numerical results indicate that the new approximations have sightly smaller L2 errors than the standard plane wave approximations. More importantly, the results are derived for more general models in inhomogeneous media.