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

DOI10.1051/m2an:2007043zbMath1140.76314OpenAlexW2161503067MaRDI QIDQ3507026

Dimitrios Mitsotakis, Jean Claude Saut, Vassilios A. Dougalis

Publication date: 18 June 2008

Published in: ESAIM: Mathematical Modelling and Numerical Analysis (Search for Journal in Brave)

Full work available at URL: http://www.numdam.org/item?id=M2AN_2007__41_5_825_0

zbMATH Keywords

error estimatesCauchy problemlocal well-posednessGalerkin finite element methods

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) Water waves, gravity waves; dispersion and scattering, nonlinear interaction (76B15) Solitary waves for incompressible inviscid fluids (76B25) Finite element methods applied to problems in fluid mechanics (76M10) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15)

Related Items (15)

Boussinesq systems in two space dimensions over a variable bottom for the generation and propagation of tsunami waves ⋮ On some Boussinesq/full dispersion systems for internal waves: numerical solution and solitary waves ⋮ The Boussinesq systems on the background of a line solitary wave ⋮ Boussinesq systems of Bona-Smith type on plane domains: theory and numerical analysis ⋮ On the numerical approximation of Boussinesq/Boussinesq systems for internal waves ⋮ The Cauchy problem on large time for surface waves Boussinesq systems ⋮ Wave breaking in Boussinesq models for undular bores ⋮ The solution of nonlinear Green-Naghdi equation arising in water sciences via a meshless method which combines moving Kriging interpolation shape functions with the weighted essentially non-oscillatory method ⋮ Regularity criterion for a Bona-Colin-Lannes system ⋮ Dispersive Shallow Water Wave Modelling. Part II: Numerical Simulation on a Globally Flat Space ⋮ Mechanical balance laws for Boussinesq models of surface water waves ⋮ Analytical and Rothe time-discretization method for a Boussinesq-type system over an uneven bottom ⋮ Boussinesq-Peregrine water wave models and their numerical approximation ⋮ A regularized shallow-water waves system with slip-wall boundary conditions in a basin: theory and numerical analysis ⋮ Extended water wave systems of Boussinesq equations on a finite interval: theory and numerical analysis

Uses Software

• ITPACK

Cites Work

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• $L^\infty $-Multivariate Approximation Theory
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