TY - JOUR
T1 - A Posteriori Error Estimates for Conservative Local Discontinuous Galerkin Methods for the Generalized Korteweg-de Vries Equation
AU - Ohannes Karakashian & Yulong Xing
JO - Communications in Computational Physics
VL - 1
SP - 250
EP - 278
PY - 2018
DA - 2018/04
SN - 20
DO - http://doi.org/10.4208/cicp.240815.301215a
UR - https://global-sci.org/intro/article_detail/cicp/11152.html
KW - 
AB - <p style="text-align: justify;">We construct and analyze conservative local discontinuous Galerkin (LDG)
methods for the Generalized Korteweg-de-Vries equation. LDG methods are designed
by writing the equation as a system and performing separate approximations to the
spatial derivatives. The main focus is on the development of conservative methods
which can preserve discrete versions of the first two invariants of the continuous solution,
and a posteriori error estimates for a fully discrete approximation that is based on
the idea of dispersive reconstruction. Numerical experiments are provided to verify
the theoretical estimates.</p>