Error Estimates for Galerkin Approximations of the Serre Equations
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Publication:5347523
DOI10.1137/16M1078355zbMath1362.65099arXiv1701.00668OpenAlexW2586563857MaRDI QIDQ5347523
Dimitrios Mitsotakis, D. C. Antonopoulos, Vassilios A. Dougalis
Publication date: 24 May 2017
Published in: SIAM Journal on Numerical Analysis (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1701.00668
error estimatessolitary wavesSerre equationssurface water wavesstandard Galerkin finite element methods
KdV equations (Korteweg-de Vries equations) (35Q53) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60)
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Numerical study of the Serre-Green-Naghdi equations and a fully dispersive counterpart ⋮ On weakly singular and fully nonlinear travelling shallow capillary-gravity waves in the critical regime ⋮ Galerkin finite element methods for the numerical solution of two classical-Boussinesq type systems over variable bottom topography ⋮ Corrigendum: Error Estimates for Galerkin Approximations of the Serre Equations
Cites Work
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- Numerical solution of the `classical' Boussinesq system
- On the Galerkin/finite-element method for the Serre equations
- Large time existence for 1D Green-Naghdi equations
- A splitting approach for the fully nonlinear and weakly dispersive Green-Naghdi model
- Asymptotic description of solitary wave trains in fully nonlinear shallow-water theory
- Numerical solution of Boussinesq systems of the Bona-Smith family
- Efficient computation of steady solitary gravity waves
- The kinematics and stability of solitary and cnoidal wave solutions of the Serre equations
- Recent advances in Serre-Green-Naghdi modelling for wave transformation, breaking and runup processes
- On the nonlinear dynamics of the traveling-wave solutions of the Serre system
- Petviashvili type methods for traveling wave computations. II: Acceleration with vector extrapolation methods
- Error estimates for the standard Galerkin-finite element method for the shallow water equations
- Finite volume and pseudo-spectral schemes for the fully nonlinear 1D Serre equations
- A Numerical Study of the Exact Evolution Equations for Surface Waves in Water of Finite Depth
- On Some High-Order Accurate Fully Discrete Galerkin Methods for the Korteweg-de Vries Equation
- Collisions between two solitary waves. Part 2. A numerical study
- On the theory of water waves
- Convergence Estimates for Galerkin Methods for Variable Coefficient Initial Value Problems
- A derivation of equations for wave propagation in water of variable depth
- Korteweg-de Vries Equation and Generalizations. III. Derivation of the Korteweg-de Vries Equation and Burgers Equation
- Error estimates for Galerkin approximations of the “classical” Boussinesq system
- Derivation of asymptotic two-dimensional time-dependent equations for surface water wave propagation
- Hamiltonian Structure and Linear Stability of Solitary Waves of the Green-Naghdi Equations
- A shallow‐water approximation to the full water wave problem
- Integrals of nonlinear equations of evolution and solitary waves
- Solitary water wave interactions
