CRPC-TR98764						May 1998

Title: Finite Element Approximations to the System of Shallow Water 
Equations, Part III: On the Treatment of Boundary Conditions

Authors: Clint N. Dawson and Monica L. Martinez

Submitted September 1998; Available as TICAM Report 98-15

Abstract:
We continue our investigation of finite element approximations to the
system of shallow water equations, based on the generalized wave
continuity equation (GWCE) formulation.  In previous work, we analyzed
this system assuming Dirichlet boundary conditions on both elevation and
velocity.  Based on physical grounds, it is possible to not impose
boundary conditions on elevation.  Thus, we examine the formulation for
the case of Dirichlet conditions on velocity only.  The changes required
to the finite element method are presented, and stability and error
estimates are derived for both an approximate linear model and a full
nonlinear model, assuming continous time. Stability for a discrete time
method is also shown.

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Clint N. Dawson			Monica L. Martinez
clint@ticam.utexas.edu		monicam@ticam.utexas.edu
Texas Institute for Computational and Applied Mathematics
University of Texas at Austin