On some Boussinesq systems in two space dimensions: theory and numerical analysis

Vassilios A. Dougalis; Dimitrios E. Mitsotakis; Jean-Claude Saut

ESAIM: Mathematical Modelling and Numerical Analysis (2007)

  • Volume: 41, Issue: 5, page 825-854
  • ISSN: 0764-583X

Abstract

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A three-parameter family of Boussinesq type systems in two space dimensions is considered. These systems approximate the three-dimensional Euler equations, and consist of three nonlinear dispersive wave equations that describe two-way propagation of long surface waves of small amplitude in ideal fluids over a horizontal bottom. For a subset of these systems it is proved that their Cauchy problem is locally well-posed in suitable Sobolev classes. Further, a class of these systems is discretized by Galerkin-finite element methods, and error estimates are proved for the resulting continuous time semidiscretizations. Results of numerical experiments are also presented with the aim of studying properties of line solitary waves and expanding wave solutions of these systems.

How to cite

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Dougalis, Vassilios A., Mitsotakis, Dimitrios E., and Saut, Jean-Claude. "On some Boussinesq systems in two space dimensions: theory and numerical analysis." ESAIM: Mathematical Modelling and Numerical Analysis 41.5 (2007): 825-854. <http://eudml.org/doc/250024>.

@article{Dougalis2007,
abstract = { A three-parameter family of Boussinesq type systems in two space dimensions is considered. These systems approximate the three-dimensional Euler equations, and consist of three nonlinear dispersive wave equations that describe two-way propagation of long surface waves of small amplitude in ideal fluids over a horizontal bottom. For a subset of these systems it is proved that their Cauchy problem is locally well-posed in suitable Sobolev classes. Further, a class of these systems is discretized by Galerkin-finite element methods, and error estimates are proved for the resulting continuous time semidiscretizations. Results of numerical experiments are also presented with the aim of studying properties of line solitary waves and expanding wave solutions of these systems. },
author = {Dougalis, Vassilios A., Mitsotakis, Dimitrios E., Saut, Jean-Claude},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {Boussinesq systems in two space dimensions; water wave theory; nonlinear dispersive wave equations; Galerkin-finite element methods for Boussinesq systems.; local well-posedness; Cauchy problem; Galerkin finite element methods; error estimates},
language = {eng},
month = {10},
number = {5},
pages = {825-854},
publisher = {EDP Sciences},
title = {On some Boussinesq systems in two space dimensions: theory and numerical analysis},
url = {http://eudml.org/doc/250024},
volume = {41},
year = {2007},
}

TY - JOUR
AU - Dougalis, Vassilios A.
AU - Mitsotakis, Dimitrios E.
AU - Saut, Jean-Claude
TI - On some Boussinesq systems in two space dimensions: theory and numerical analysis
JO - ESAIM: Mathematical Modelling and Numerical Analysis
DA - 2007/10//
PB - EDP Sciences
VL - 41
IS - 5
SP - 825
EP - 854
AB - A three-parameter family of Boussinesq type systems in two space dimensions is considered. These systems approximate the three-dimensional Euler equations, and consist of three nonlinear dispersive wave equations that describe two-way propagation of long surface waves of small amplitude in ideal fluids over a horizontal bottom. For a subset of these systems it is proved that their Cauchy problem is locally well-posed in suitable Sobolev classes. Further, a class of these systems is discretized by Galerkin-finite element methods, and error estimates are proved for the resulting continuous time semidiscretizations. Results of numerical experiments are also presented with the aim of studying properties of line solitary waves and expanding wave solutions of these systems.
LA - eng
KW - Boussinesq systems in two space dimensions; water wave theory; nonlinear dispersive wave equations; Galerkin-finite element methods for Boussinesq systems.; local well-posedness; Cauchy problem; Galerkin finite element methods; error estimates
UR - http://eudml.org/doc/250024
ER -

References

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