Wave Propagation in Quadratic-Finite-Element Approximations to Hyperbolic Equations

Eigenmodes for the quadratic-finite-element method (QFEM) are expressed as a linear combination of two conventional semi-discrete Fourier modes. Each of these Fourier modes moves at a different phase speed, but both modes have the same group velocity. This representation of the QFEM eigenmodes clarifies the significance of the negative phase speeds that naturally arise as part of the conventional analysis.