Conservative, discontinuous Galerkin-methods for the generalized korteweg-de vries equation
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 L2-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.© 2013 American Mathematical Society.
Mathematics of Computation
Bona, J., Chen, H., Karakashian, O., & Xing, Y. (2013). Conservative, discontinuous Galerkin-methods for the generalized korteweg-de vries equation. Mathematics of Computation, 82 (283), 1401-1432. https://doi.org/10.1090/S0025-5718-2013-02661-0