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

被引：0
|
作者：
V. A. Dougalis
D. E. Mitsotakis
J.-C. Saut
机构：
[1] University of Athens,Department of Mathematics
[2] Institute of Applied and Computational Mathematics FO.R.T.H.,UMR de Mathématiques
[3] Université de Paris-Sud,undefined
来源：
Journal of Scientific Computing | 2010年 / 44卷
关键词：
Boussinesq systems; Nonlinear dispersive wave equations; Initial-boundary-value problems; Galerkin-finite element methods for Boussinesq systems;
D O I：
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学科分类号：
摘要：
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 L2 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.
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页码：109 / 135
页数：26
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