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Error estimates for Galerkin approximations of the ``classical'' Boussinesq system

Authors: D. C. Antonopoulos and V. A. Dougalis
Journal: Math. Comp. 82 (2013), 689-717
MSC (2010): Primary 65M60, 35Q53
Published electronically: December 12, 2012
MathSciNet review: 3008835
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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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D. C. Antonopoulos
Affiliation: Department of Mathematics, University of Athens, 15784 Zographou, Greece

V. A. Dougalis
Affiliation: Department of Mathematics, University of Athens, 15784 Zographou, Greece – and – Institute of Applied and Computational Mathematics, FORTH, 70013 Heraklion, Greece

Keywords: Boussinesq systems, nonlinear dispersive waves, first-order hyperbolics, Galerkin methods, error estimates
Received by editor(s): August 26, 2010
Received by editor(s) in revised form: October 6, 2011
Published electronically: December 12, 2012
Article copyright: © Copyright 2012 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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