A Hamiltonian approximation to simulate solitary waves of the Korteweg-de Vries equation

Author:
Ming You Huang

Journal:
Math. Comp. **56** (1991), 607-620

MSC:
Primary 65M60; Secondary 35Q53, 76B15, 76B25

MathSciNet review:
1068815

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Abstract: Given the Hamiltonian nature and conservation laws of the Korteweg-de Vries equation, the simulation of the solitary waves of this equation by numerical methods should be effected in such a way as to maintain the Hamiltonian nature of the problem. A semidiscrete finite element approximation of Petrov-Galerkin type, proposed by R. Winther, is analyzed here. It is shown that this approximation is a finite Hamiltonian system, and as a consequence, the energy integral

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Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1991-1068815-X

Keywords:
Korteweg-de Vries equation,
finite element method,
Hamiltonian approximation,
superconvergence

Article copyright:
© Copyright 1991
American Mathematical Society