AbstractWhen hyperbolic partial differential equations are replaced by numerical finite-difference or finite element approximations, one of the spurious effects is where to introduce errors in the characteristic velocities of these equations. If solutions are locally considered as the superposition of sinusoidal components of different spatial frequency w, then, assuming linearity, the numerical approximation generally preserves the sinusoidal nature of each component, but affects the velocity by an error, which varies with w.
This frequency dependence of the velocity results in spurious dispersion phenomena, which are most apparent for solutions, which contain sharp spatial variations.
Under certain conditions the presence of such sharp variations creates spurious oscillations of wavelength. Such spurious oscillations may then be observed to propagate as "packets"; with a group velocity which may be predicted by a theoretical analysis of the numerical algorithms. One area where these phenomena are particularly apparent is in geophysical fluid dynamics equations, in which natural dissipation is small, and, as a result spurious oscillations in numerical solutions are likely to persist over long periods of time.
The mathematics, which describes those spurious phenomena together with numerical experiments, which verify the theory, are given in this paper.*
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