Numerical dispersion of higher order nodal elements in the finite-element method

The discretization inherent in the finite-element method results in numerical dispersion. This dispersion is investigated for a time-harmonic plane wave propagating through an infinite, two-dimensional, finite-element mesh composed of uniform quadrilateral and triangular elements. The effects on the dispersion due to the propagation direction of the wave, the order of the elements, the node density, and the mesh geometry are studied. Results are given which can serve as a guide in selecting the appropriate element order, node density, and mesh geometry when applying the finite-element method.