Finite Element Approximations to the System of Shallow Water Equations, Part III: On the Treatment of Boundary Conditions

We continue our investigation of nite element approximations to the system of shallow water equations, based on the generalized wave continuity equation (GWCE) formulation. In previous work, we analyzed this system assuming Dirichlet boundary conditions on both elevation and velocity. Based on physicalgrounds, it is possible to not impose boundaryconditionson elevation. Thus, we examine the formulation for the case of Dirichlet conditions on velocity only. The changes required to the nite element method are presented, and stability and error estimates are derived for both an approximate linear model and a full nonlinear model, assuming continous time. Stability for a discrete time method is also shown.