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Volume 20, Issue 1
A Posteriori Error Estimates for Conservative Local Discontinuous Galerkin Methods for the Generalized Korteweg-de Vries Equation

Ohannes Karakashian & Yulong Xing

DOI: 10.4208/cicp.240815.301215a

Commun. Comput. Phys., 20 (2016), pp. 250-278.

Published online: 2018-04

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  • Abstract

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.

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@Article{CiCP-20-250, author = {Ohannes Karakashian and Yulong Xing}, title = {A Posteriori Error Estimates for Conservative Local Discontinuous Galerkin Methods for the Generalized Korteweg-de Vries Equation}, journal = {Communications in Computational Physics}, year = {2018}, volume = {20}, number = {1}, pages = {250--278}, abstract = {

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.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.240815.301215a}, url = {http://global-sci.org/intro/article_detail/cicp/11152.html} }
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 -

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.

Ohannes Karakashian and Yulong Xing. (2018). A Posteriori Error Estimates for Conservative Local Discontinuous Galerkin Methods for the Generalized Korteweg-de Vries Equation. Communications in Computational Physics. 20 (1). 250-278. doi:10.4208/cicp.240815.301215a
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