Conservative, discontinuous Galerkin–methods for the generalized Korteweg–de Vries equation

Bona, J.; Chen, H.; Karakashian, O.; Xing, Y.

doi:10.1090/S0025-5718-2013-02661-0

Conservative, discontinuous Galerkin-methods for the generalized Korteweg-de Vries equation

Authors: J. L. Bona, H. Chen, O. Karakashian and Y. Xing
Journal: Math. Comp. 82 (2013), 1401-1432
MSC (2010): Primary 65N12, 65N30, 35Q35, 35Q51, 35Q53, 35Q86, 76B15, 76B25
DOI: https://doi.org/10.1090/S0025-5718-2013-02661-0
Published electronically: January 7, 2013
MathSciNet review: 3042569
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Abstract: We construct, analyze and numerically validate a class of conservative, discontinuous Galerkin schemes for the Generalized Korteweg-de Vries equation. Up to round-off error, these schemes preserve discrete versions of the first two invariants (the integral of the solution, usually identified with the mass, and the -norm) of the continuous solution. Numerical evidence is provided indicating that these conservation properties impart the approximations with beneficial attributes, such as more faithful reproduction of the amplitude and phase of traveling-wave solutions. The numerical simulations also indicate that the discretization errors grow only linearly as a function of time.

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