Finite Element Approximations to the System of Shallow Water Equations, Part II: Discrete-Time A Priori Error Estimates

Various sophisticated finite element models for surface water flow exist in the literature. Gray, Kolar, Luettich, Lynch, and Westerink have developed a hydrodynamic model based on the generalized wave continuity equation (GWCE) formulation and have formulated a Galerkin finite element procedure based on combining the GWCE with the nonconservative momentum equations. Numerical experiments suggest that this method is robust and accurate and suppresses spurious oscillations which plague other models. In this paper, we analyze a closely related Galerkin method which uses the conservative momentum equations (CME). For this GWCE--CME system of equations, we present, for discrete time, an a priori error estimate based on an ${\cal L}^{2}$ projection.