### Abstract

We consider the dispersive properties of Galerkin finite element methods for wave propagation. The dispersive properties of conforming finite element scheme are analysed in the setting of the Helmholtz equation and an explicit form the discrete dispersion relation is obtained for elements of arbitrary order. It is shown that the numerical dispersion displays three different types of behaviour depending on the order of the polynomials used relative to the mesh-size and the wave number. Quantitative estimates are obtained for the behaviour and rates of decay of the dispersion error in the differing regimes.