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

2010/08/25 by Antonopoulos, D. C., Dougalis, V. A.
#35Q53 #65M60 #FOS: Mathematics #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.1008.4248

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.

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