Cn. Dawson et Ml. Martinez-canales, A characteristic-Galerkin approximation to a system of shallow water equations, NUMER MATH, 86(2), 2000, pp. 239-256
Characteristic methods are known to handle advective flow better than tradi
tional Galerkin methods and allow large time steps to be taken when compare
d to standard time-stepping methods. In this paper, we investigate a charac
teristic-Galerkin approximation to the 2-dimensional system of shallow wate
r equations. We derive L-infinity ((0; T); L-2(Omega)) bounds for elevation
and velocity, showing these to be optimal for velocity in L-2 ((0, T); H-1
(Omega)).