CRPC-TR98769-S						September 1998

Title: Stability and Error Analysis of the Finite Element Models of the 
1-D Shallow Water Equations

Author: Sharon Ann Lozano

Submitted September 1998; Available as UT-Austin Senior Thesis

Abstract:
Interest in the numerical solutions of shallow water equations has grown 
in recent years. Shallow water equations predict tidal elevation and 
velocities in bodies such as bays and estuaries. The circulations 
patterns obtained can be used to determine contaminant propagation in 
coastal areas. In this paper, we provide stability and error analysis for 
the 1-dimensional linearized shallow water equations. We derive L~(L^2) 
stability estimates for the Galerkin finite element approximation of the 
wave formulation in continuous time. We also derive L~(L^2) error 
estimates for elevation and velocity which are optimal in L~(H^1). In 
addition, we successfully develop a Chorin-type projection 
operator-splitting scheme, using finite difference time-stepping, for the 
primitive formulation. We also develop a stability estimate which seems 
to be the first of its kind and a significant literary contribution.

------------------------------------------------------------------------------
Sharon Ann Lozano
sharon@ticam.utexas.edu
Texas Institute for Computational and Applied Mathematics
University of Texas at Austin