Wave propagation in quadratic-finite-element approximations to hyperbolic equations (Q1976847)

The author discusses the dispersion relation for discretization of the wave equation \(u_t + c u_x = 0\) by the method of lines derived from application of the finite-element method with quadratic basis functions. For many discretizations of this wave equation the dispersion function is periodic with period \(2 \pi\), but in this case the period is \(4 \pi\). On an interval of length \(2 \pi\) one obtains what appear to be two dispersion relations, but they map into each other under a translation by~\(2 \pi\).