Finite Element Approximations to the System of Shallow Water Equations I: Continuous-Time A Priori Error Estimates

Abstract

Various sophisticated finite element models for surface water flow based on the shallow water equations 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. We analyze a slightly modified Galerkin model which uses the conservative momentum equations (CME). For this GWCE-CME system of equations, we present a continuous-time a priori error estimate based on an $\asl^{2}$ projection.