Conservative Galerkin methods for dispersive Hamiltonian problems
Numerical Analysis
2021-06-15 v3 Numerical Analysis
Abstract
An energy conservative discontinuous Galerkin scheme for a generalised third order KdV type equation is designed. Based on the conservation principle, we propose techniques that allow for the derivation of optimal a priori bounds for the linear KdV equation and a posteriori bounds for the linear and modified KdV equation. Extensive numerical experiments showcasing the good long time behaviour of the scheme are summarised which are in agreement with the analysis proposed.
Cite
@article{arxiv.1811.09999,
title = {Conservative Galerkin methods for dispersive Hamiltonian problems},
author = {James Jackaman and Tristan Pryer},
journal= {arXiv preprint arXiv:1811.09999},
year = {2021}
}