Boussinesq Systems of Bona-Smith Type on Plane Domains: Theory and Numerical Analysis

Authors:
V. A. Dougalis;D. E. Mitsotakis;J. -C. Saut
Affiliations:
Department of Mathematics, University of Athens, Zographou, Greece 15784 and Institute of Applied and Computational Mathematics FO.R.T.H., Heraklion, Greece 70013;UMR de Mathématiques, Université de Paris-Sud, Orsay, France 91405;UMR de Mathématiques, Université de Paris-Sud, Orsay, France 91405
Venue:
Journal of Scientific Computing
Year:
2010

Citing 3
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Finite Element Method for Elliptic Problems

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Numerical solution of Boussinesq systems of the Bona--Smith family

Applied Numerical Mathematics

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Abstract

We consider a class of Boussinesq systems of Bona-Smith type in two space dimensions approximating surface wave flows modelled by the three-dimensional Euler equations. We show that various initial-boundary-value problems for these systems, posed on a bounded plane domain are well posed locally in time. In the case of reflective boundary conditions, the systems are discretized by a modified Galerkin method which is proved to converge in L 2 at an optimal rate. Numerical experiments are presented with the aim of simulating two-dimensional surface waves in realistic (plane) domains with a variety of initial and boundary conditions, and comparing numerical solutions of Bona-Smith systems with analogous solutions of the BBM-BBM system.