CRPC-TR97690							February 1997

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

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

Abstract:
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, accurate and suppresses spurious oscillations which plague other 
models. In this paper, we anlyze 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 L^2 projection.

Key Words: shallow water equations, surface flow, mass conservation, 
	momentum conservation, finite element model, error estimate stability

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