@Article{CiCP-10-2,
author = {},
title = {Local Discontinuous Galerkin Methods for the Degasperis-Procesi Equation},
journal = {Communications in Computational Physics},
year = {2011},
volume = {10},
number = {2},
pages = {474--508},
abstract = {<p style="text-align: justify;">In this paper, we develop, analyze and test local discontinuous Galerkin
(LDG) methods for solving the Degasperis-Procesi equation which contains nonlinear
high order derivatives, and possibly discontinuous or sharp transition solutions. The
LDG method has the flexibility for arbitrary <em>h</em>&nbsp;and <em>p</em> adaptivity. We prove the L<sup>2&nbsp;</sup>stability
for general solutions. The proof of the total variation stability of the schemes
for the piecewise constant P<sup>0&nbsp;</sup>case is also given. The numerical simulation results for
different types of solutions of the nonlinear Degasperis-Procesi equation are provided
to illustrate the accuracy and capability of the LDG method.</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.300410.300710a},
url = {https://global-sci.com/article/80931/local-discontinuous-galerkin-methods-for-the-degasperis-procesi-equation}
}