S. Chippada et al., Finite element approximations to the system of shallow water equations, part II: Discrete-time a priori error estimates, SIAM J NUM, 36(1), 1998, pp. 226-250
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 (GW
CE) formulation and have formulated a Galerkin finite element procedure bas
ed on combining the GWCE with the nonconservative momentum equations. Numer
ical experiments suggest that this method is robust and accurate and suppre
sses spurious oscillations which plague other models. In this paper, we ana
lyze a closely related Galerkin method which uses the conservative momentum
equations (CME). For this GWCE-CME system of equations, we present, for di
screte time, an a priori error estimate based on an L-2 projection.