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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

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
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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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Additional Information

D. C. Antonopoulos
Affiliation: Department of Mathematics, University of Athens, 15784 Zographou, Greece
Email: antonod@math.uoa.gr

V. A. Dougalis
Affiliation: Department of Mathematics, University of Athens, 15784 Zographou, Greece – and – Institute of Applied and Computational Mathematics, FORTH, 70013 Heraklion, Greece
Email: doug@math.uoa.gr

DOI: http://dx.doi.org/10.1090/S0025-5718-2012-02663-9
PII: S 0025-5718(2012)02663-9
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.