From the summary: The application of discrete solution methods to the second-order wave equation can yield a dispersive representation of the non-dispersive wave propagation problem resulting in a phase speed that depends not only upon the wavelength of the signal being propagated, but also upon the direction of propagation. In this work, the dependence of the dispersive errors on the wave propagation direction, mesh aspect ratio and wave number is investigated with the goal of understanding and hopefully reducing the phase and group errors associated with the two-dimensional bilinear finite element. An analysis of the dispersive effects associated with the consistent, row-sum lumped and higher-order mass matrices has led to a reduced-coupling ‘penta-diagonal’ mass matrix that yields improved phase and group errors with respect so wavelength and propagation direction. The influence of row-sum lumping mass matrix is demonstrated to always introduce lagging phase and group error, while a linear combination of the lumped and consistent mass matrices, i.e. a higher-order mass matrix, is shown to improve the dispersion characteristics of both the reduced and full-integration element.