A finite element method for extended KdV equations
From MaRDI portal
Publication:328887
DOI10.1515/amcs-2016-0039zbMath1347.65153arXiv1604.04105OpenAlexW2338456806MaRDI QIDQ328887
Maciej Szczeciński, Piotr Rozmej, Anna Karczewska, Bartosz Boguniewicz
Publication date: 21 October 2016
Published in: International Journal of Applied Mathematics and Computer Science (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1604.04105
finite element methodPetrov-Galerkin methodnonlinear equationssecond order KdV equationsshallow water wave problem
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)
Related Items
A finite element method for extended KdV equations ⋮ Accurate gradient computations at interfaces using finite element methods ⋮ A dynamic bi-orthogonal field equation approach to efficient Bayesian inversion ⋮ Element partition trees for \(h\)-refined meshes to optimize direct solver performance. I: Dynamic programming ⋮ Unnamed Item
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- A finite element method for extended KdV equations
- A direct discontinuous Galerkin method for the generalized Korteweg-de Vries equation: energy conservation and boundary effect
- Solitary wave transformation on the underwater step: asymptotic theory and numerical experiments
- Analytical and numerical aspects of certain nonlinear evolution equations. III. Numerical, Korteweg-de Vries equation
- A boundary value problem for the KdV equation: comparison of finite-difference and Chebyshev methods
- Unidirectional waves over slowly varying bottom. II: Quasi-homogeneous approximation of distorting waves
- Uni-directional waves over slowly varying bottom. I: Derivation of a KdV- type of equation
- Numerical simulation of the stochastic Korteweg-de Vries equation
- On the formulation of mass, momentum and energy conservation in the KdV equation
- Numerical method satisfying the first two conservation laws for the Korteweg-de Vries equation
- A dual-Petrov-Galerkin method for the Kawahara-type equations
- On Stability of Some Finite Difference Schemes for the Korteweg-de Vries Equation
- Conservative, discontinuous Galerkin–methods for the generalized Korteweg–de Vries equation
- On the evolution of packets of water waves
- Interaction of "Solitons" in a Collisionless Plasma and the Recurrence of Initial States
- The extended Korteweg-de Vries equation and the resonant flow of a fluid over topography
- Solitary wave dynamics in shallow water over periodic topography
- Modulation theory solution for resonant flow over topography
- A derivation of equations for wave propagation in water of variable depth
- A numerical and theoretical study of certain nonlinear wave phenomena
- Different approximations of shallow fluid flow over an obstacle
- Nonlinear Waves, Solitons and Chaos
- Resonant flow of a stratified fluid over topography
- Korteweg-de Vries Equation and Generalizations. II. Existence of Conservation Laws and Constants of Motion
- Soliton interaction for the extended Korteweg-de Vries equation
- Ordering of two small parameters in the shallow water wave problem
- The solitary wave in water of variable depth
- Fission of a weakly nonlinear interfacial solitary wave at a step
- A derivation of the Green-Naghdi equations for irrotational flows
