Convergence of the Splitting Method for Shallow Water Equations

In this paper we analyze the convergence of the splitting method for shallow water equations. In particular, we give an analytical estimation of the time step which is necessary for the convergence and then we study the behaviour of the motion of the shallow water in the Venice lagoon by using the splitting method with a finite element space discretization. The numerical calculations show that the splitting method is convergent if the time step of the first part is sufficiently small and that it gives a good agreement with the experimental data.