Journal
MATHEMATICS OF COMPUTATION
Volume 82, Issue 283, Pages 1401-1432Publisher
AMER MATHEMATICAL SOC
DOI: 10.1090/S0025-5718-2013-02661-0
Keywords
Discontinuous Galerkin methods; Korteweg-de Vries equation; error estimates; conservation laws
Categories
Funding
- INRIA at the Universite Bordeaux 1, France
- NSF [DMS-0811314]
- Office of Advanced Scientific Computing Research, U.S. Department of Energy
- UT-Battelle, LLC [DE-AC05-00OR22725]
- Direct For Mathematical & Physical Scien
- Division Of Mathematical Sciences [1216740] Funding Source: National Science Foundation
Ask authors/readers for more resources
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.
Authors
I am an author on this paper
Click your name to claim this paper and add it to your profile.
Reviews
Recommended
No Data Available