AbstractThis paper presents new finite element formulations of the shallow‐water wave equations which use different basis functions for the velocity and height fields. These arrangements are analysed with the Fourier transform technique which was developed by Schoenstadt,1and they are also compared with other finite difference and finite element schemes. The new schemes are integrated in time for two initial states and compared with analytic solutions and numerical solutions from other schemes. The behaviour of the new forms is excellent and they are also convenient to apply in two dimensions with triangular element