TY - JOUR
T1 - Local Discontinuous Galerkin Methods for the Degasperis-Procesi Equation
AU - Yan Xu & Chi-Wang Shu
JO - Communications in Computational Physics
VL - 2
SP - 474
EP - 508
PY - 2011
DA - 2011/10
SN - 10
DO - http://doi.org/10.4208/cicp.300410.300710a
UR - https://global-sci.org/intro/article_detail/cicp/7451.html
KW - 
AB - <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>