An investigation of numerical dispersion in the vector finite element method using quadrilateral elements

The discretization inherent in the vector finite element method results in the numerical dispersion of a propagating wave. The numerical dispersion of a time-harmonic plane wave propagating through an infinite, two-dimensional, vector finite element mesh composed of uniform quadrilateral elements is investigated. The effects on the numerical dispersion of the propagation direction of the wave, the order of the polynomials used for the basis functions, and the electrical size of the elements are investigated. Simple formulas are presented which are excellent approximations to the exact numerical dispersion. The numerical dispersion is validated by a numerical example