Dispersion analysis of a non-conforming finite element method for the Helmholtz and elastodynamic equations

We investigate the dispersive properties of a non-conforming nite element method to solve the twodimensional Helmholtz and elastodynamics equations. The study is performed by deriving and analysing the dispersion relations and by evaluating the derived quantities, such as the dimensionless phase and group velocities. Also the phase di erence between exact and numerical solutions is investigated. The studied method, which yields a linear spatial approximation, is shown to be less dispersive than a conforming bilinear nite element method in the two cases shown herein. Moreover, it almost halves the number of points per wavelength necessary to reach a given accuracy when calculating the mentioned velocities in both cases here presented