TY - JOUR
T1 - Conservative and Dissipative Local Discontinuous Galerkin Methods for Korteweg-de Vries Type Equations
AU - Qian Zhang & Yinhua Xia
JO - Communications in Computational Physics
VL - 2
SP - 532
EP - 563
PY - 2018
DA - 2018/10
SN - 25
DO - http://doi.org/10.4208/cicp.OA-2017-0204
UR - https://global-sci.org/intro/article_detail/cicp/12762.html
KW - Local discontinuous Galerkin method, conservative and dissipative schemes, Korteweg-de Vries type equations, semi-implicit spectral deferred correction method.
AB - <p style="text-align: justify;">In this paper, we develop the Hamiltonian conservative and $L^2$ conservative
local discontinuous Galerkin (LDG) schemes for the Korteweg-de Vries (KdV) type
equations with the minimal stencil. For the time discretization, we adopt the semi-implicit
spectral deferred correction (SDC) method to achieve the high order accuracy
and efficiency. Also we compare the schemes with the dissipative LDG scheme. Stability
of the fully discrete schemes is provided by Fourier analysis for the linearized KdV
equation. Numerical examples are shown to illustrate the capability of these schemes.
Compared with the dissipative LDG scheme, the numerical simulations also indicate
that the conservative LDG scheme with high order time discretization can reduce the
long time phase error validly.</p>