Numerically induced oscillations in finite element approximations to the shallow water equations

Numerical noise has been a problem with finite element solutions to the shallow water equations. Two methods used to reduce the noise level are evaluated, and these results are compared with published results for equal‐order interpolations. The two methods are mixed‐interpolation (quadratic interpolation for velocity and linear interpolation for sea level) and a spectral form of the wave equation. Whereas mixed interpolation removes the troublesome sea level mode, it can still have considerable noise in velocity. The spectral wave equation is efficient and does not contain the spurious eigenmodes which contribute to high noise levels.