A Hamiltonian approximation to simulate solitary waves of the Kortewegde Vries equation
Author:
Ming You Huang
Journal:
Math. Comp. 56 (1991), 607620
MSC:
Primary 65M60; Secondary 35Q53, 76B15, 76B25
MathSciNet review:
1068815
Fulltext PDF Free Access
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Abstract: Given the Hamiltonian nature and conservation laws of the Kortewegde 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 PetrovGalerkin 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 is exactly conserved by this method. In addition, there is a discussion of error estimates and superconvergence properties of the method, in which there is no perturbation term but instead a suitable choice of initial data. A singlestep fully discrete scheme, and some numerical results, are presented.
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Additional Information
DOI:
http://dx.doi.org/10.1090/S0025571819911068815X
PII:
S 00255718(1991)1068815X
Keywords:
Kortewegde Vries equation,
finite element method,
Hamiltonian approximation,
superconvergence
Article copyright:
© Copyright 1991 American Mathematical Society
