Integrations of the primitive equations on a sphere using the finite element method

Integrations of the shallow water equations on the sphere using the finite element method are performed and compared with published integrations of Doron et al. (1974). Better results are obtained with the finite element method than with a second order finite difference method using four times the number of grid points, in particular the breakdown of a Rossby wave of zonal wavenumber 8 is correctly predicted.