Boussinesq systems of Bona-Smith type on plane domains: theory and numerical analysis

DOI10.1007/s10915-010-9368-zzbMath1203.65179arXiv0907.4918OpenAlexW2003315898MaRDI QIDQ618595

Dimitrios Mitsotakis, Jean Claude Saut, Vassilios A. Dougalis

Publication date: 16 January 2011

Published in: Journal of Scientific Computing (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0907.4918

zbMATH Keywords

initial-boundary-value problemsnonlinear dispersive wave equationsBoussinesq systemsGalerkin-finite element methods for Boussinesq systems

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) 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)

Related Items (10)

Quintic B-spline collocation method for the numerical solution of the Bona-Smith family of Boussinesq equation type ⋮ Modeling shallow water waves ⋮ Blowup of solutions of nonlinear equations and systems of nonlinear equations in wave theory ⋮ Dispersive Shallow Water Wave Modelling. Part I: Model Derivation on a Globally Flat Space ⋮ Analytical and Rothe time-discretization method for a Boussinesq-type system over an uneven bottom ⋮ Error estimates for a fully discrete spectral scheme for nonlinear Boussinesq systems ⋮ Boussinesq-Peregrine water wave models and their numerical approximation ⋮ Stability analysis for a fully discrete spectral scheme for Boussinesq systems ⋮ 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

Cites Work

• Numerical solution of Boussinesq systems of the Bona-Smith family
• Numerical investigation of a two-dimensional Boussinesq system
• On initial-boundary value problems for a Boussinesq system of BBM-BBM type in a plane domain
• Initial-boundary-value problems for the Bona-Smith family of Boussinesq systems
• Boussinesq equations and other systems for small-amplitude long waves in nonlinear dispersive media. I: Derivation and linear theory
• A Boussinesq system for two-way propagation of nonlinear dispersive waves
• Periodic wave patterns of two-dimensional Boussinesq systems
• Long wave approximations for water waves
• On some Boussinesq systems in two space dimensions: theory and numerical analysis
• The Stability in L p and W p 1 of the L 2 -Projection onto Finite Element Function Spaces
• A model for the two-way propagation of water waves in a channel
• Optimal L ∞ Estimates for the Finite Element Method on Irregular Meshes
• Boussinesq equations and other systems for small-amplitude long waves in nonlinear dispersive media: II. The nonlinear theory

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