A Galerkin least squares method for time harmonic Maxwell equations using Nédélec elements

A Galerkin least squares finite element method for the solution of the time-harmonic Maxwell’s equations using Nédélec elements is proposed. This method appends a least-squares term, evaluated within element interiors, to the standard Galerkin method. For the case of lowest order hexahedral element, the numerical parameter multiplying this term is determined so as to optimize the dispersion properties of the resulting formulation. In particular, explicit expressions for this parameter are derived that lead to methods with no dispersion error for propagation along a specified direction and reduced dispersion error over all directions. It is noted that this method is easy to implement and does not add to the computational costs of the standard Galerkin method. The performance of this method is tested on problems of practical interest.