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

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

2010-08-25

arxiv.org/abs/1008.4248v1

Mathematics

Numerical Analysis

61 pages, 2 figures, 12 tables

Scientific paper

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.

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