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.
Mots-clés : Boussinesq systems in two space dimensions, water wave theory, nonlinear dispersive wave equations, Galerkin-finite element methods for Boussinesq systems
@article{M2AN_2007__41_5_825_0,
author = {Dougalis, Vassilios A. and Mitsotakis, Dimitrios E. and Saut, Jean-Claude},
title = {On some {Boussinesq} systems in two space dimensions : theory and numerical analysis},
journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique},
pages = {825--854},
publisher = {EDP-Sciences},
volume = {41},
number = {5},
year = {2007},
doi = {10.1051/m2an:2007043},
mrnumber = {2363885},
zbl = {1140.76314},
language = {en},
url = {http://archive.numdam.org/articles/10.1051/m2an:2007043/}
}
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: Modélisation mathématique et analyse numérique PY - 2007 SP - 825 EP - 854 VL - 41 IS - 5 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/m2an:2007043/ DO - 10.1051/m2an:2007043 LA - en ID - M2AN_2007__41_5_825_0 ER -
%0 Journal Article %A Dougalis, Vassilios A. %A Mitsotakis, Dimitrios E. %A Saut, Jean-Claude %T On some Boussinesq systems in two space dimensions : theory and numerical analysis %J ESAIM: Modélisation mathématique et analyse numérique %D 2007 %P 825-854 %V 41 %N 5 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/m2an:2007043/ %R 10.1051/m2an:2007043 %G en %F M2AN_2007__41_5_825_0
Dougalis, Vassilios A.; Mitsotakis, Dimitrios E.; Saut, Jean-Claude. On some Boussinesq systems in two space dimensions : theory and numerical analysis. ESAIM: Modélisation mathématique et analyse numérique, Tome 41 (2007) no. 5, pp. 825-854. doi : 10.1051/m2an:2007043. http://archive.numdam.org/articles/10.1051/m2an:2007043/
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