Notes on error estimates for Galerkin approximations of the 'classical' Boussinesq system and related hyperbolic problems
Provides rigorous error analysis for numerical methods used in modeling nonlinear dispersive waves, which is incremental for the field of numerical analysis of hyperbolic problems.
The paper proves error estimates for Galerkin-finite element discretizations of the classical Boussinesq system and its symmetric analog, with theoretical convergence orders consistent with numerical experiments.
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.