CRPC-TR97689							February 1997

Title: Finite Element Approximation to the System of Shallow Water 
	Equations, Part I: Continuous Time A Priori Error Estimates

Authors: S. Chippada, C. Dawson, M. Martinez, M. Wheeler

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, 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 
estimate based on an L^2 projection.

Key Words: shallow water equations, surface water flow, mass 
	conservation, momentum conservation, finite element method, a priori 
	error estimate

AMS Subject Classifications: 35Q35, 35L65, 65N30, 65N15