Abstract
Recent analyses of spurious phenomena near interfaces and boundaries of numerical approximations of hyperbolic equations have produced a host of interesting, concrete results, which are reviewed in this paper. What characterizes these analyses is that they rely on tools of mathematical physics, in particular in the systematic use of Fourier transforms and the concept of sinusoidal wave propagation this leads to a description of numerical inaccuracy in terms of dispersion, and a description of spurious numerical solutions in terms of wave packets and group velocities. It is in providing the mathematics needed to describe spurious reflection at numerical boundaries and at interfaces in mesh refinement that the most applied results of this theory are obtained.