Conservative, discontinuous Galerkin–methods for the generalized Korteweg–de Vries equation
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- by J. L. Bona, H. Chen, O. Karakashian and Y. Xing
- Math. Comp. 82 (2013), 1401-1432
- DOI: https://doi.org/10.1090/S0025-5718-2013-02661-0
- Published electronically: January 7, 2013
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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 $L^2$–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.References
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Bibliographic Information
- J. L. Bona
- Affiliation: Department of Mathematics, Statistics and Computer Science, The University of Illinois at Chicago, Chicago, Illinois 60607
- Email: bona@math.uic.edu
- H. Chen
- Affiliation: Department of Mathematical Sciences, The University of Memphis, Memphis, Tennessee 38152
- Email: hchen1@memphis.edu
- O. Karakashian
- Affiliation: Department of Mathematics, The University of Tennessee, Knoxville, Tennessee 37996
- Email: ohannes@math.utk.edu
- Y. Xing
- Affiliation: Department of Mathematics, The University of Tennessee, Knoxville, Tennessee 37996 – and – the Computer Science and Mathematics Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831
- MR Author ID: 761305
- Email: xingy@math.utk.edu
- Received by editor(s): June 7, 2011
- Received by editor(s) in revised form: December 6, 2011
- Published electronically: January 7, 2013
- © Copyright 2013
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - 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
- MathSciNet review: 3042569