Finite element approximations to the system of shallow water equations, part III: on the treatment of boundary conditions

摘要

We continue our investigation of finite 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 physical grounds, it is possible to not impose boundary conditions on elevation. Thus we examine the formulation for the case of Dirichlet conditions on velocity only. The changes required to the finite element method are presented, and stability and error estimates are derived for an approximate linear model, assuming continuous time. Stability for a discrete time method is also shown. [References: 9]