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

Abstract

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.

61 pages, 2 figures, 12 tables

Cited by in corpus (2)

• Boussinesq-Peregrine water wave models and their numerical approximation
• Notes on error estimates for the standard Galerkin-finite element method for the Shallow Water equations