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We consider the `classical' Boussinesq system in one space dimension and itssymmetric analog. These systems model two-way propagation of nonlinear,dispersive long waves of small amplitude on the surface of an ideal fluid in auniform horizontal channel. We discretize an initial-boundary-value problem forthese systems in space using Galerkin-finite element methods and prove errorestimates for the resulting semidiscrete problems and also for their fullydiscrete analogs effected by explicit Runge-Kutta time-stepping procedures. Thetheoretical orders of convergence obtained are consistent with the results ofnumerical experiments that are also presented.

Notes on error estimates for Galerkin approximations of the 'classical' Boussinesq system and related hyperbolic problems