%0 Journal Article
%T Notes on error estimates for Galerkin approximations of the 'classical' Boussinesq system and related hyperbolic problems
%A D. C. Antonopoulos
%A V. A. Dougalis
%J Mathematics
%D 2010
%I arXiv
%X We consider the `classical' Boussinesq system in one space dimension and its symmetric analog. These systems model two-way propagation of nonlinear, dispersive long waves of small amplitude on the surface of an ideal fluid in a uniform horizontal channel. We discretize an initial-boundary-value problem for these systems in space using Galerkin-finite element methods and prove error estimates for the resulting semidiscrete problems and also for their fully discrete analogs effected by explicit Runge-Kutta time-stepping procedures. The theoretical orders of convergence obtained are consistent with the results of numerical experiments that are also presented.
%U http://arxiv.org/abs/1008.4248v1