ABSTRACT
An algorithm is described here to study a shallow water model for a lagoon by a Finite Element approach making use of a TaylorGalerkin formulation . The mathematical model to study the motion in a lagoon consist of the continuity equation and the Navier-Stokes equations. The 3D-problem is reduced to a 2-dimensional problem through a vertical integration and is solved using a finite element method. The case treated is a long wave in the assumption that n<<H where 11 and H are respectively the water elevation and the
depth. To determine the values of the unknowns, velocity into the horizontal direction and elevat~on along the vertical direction, the Finite Element Method is appfied in a Galerkin residual form. The formulation is tightly related to the geometry of the problem studied. The discretization parameters have been carefully refined and interesting examples have been applied to the Venice lagoon.
