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A hybrid LDG-HWENO scheme for KdV-type equations

Authors
  • Luo, Dongmi
  • Huang, Weizhang
  • Qiu, Jianxian
Type
Published Article
Publication Date
Nov 13, 2015
Submission Date
Nov 13, 2015
Identifiers
DOI: 10.1016/j.jcp.2016.02.064
Source
arXiv
License
Yellow
External links

Abstract

A hybrid LDG-HWENO scheme is proposed for the numerical solution of KdV-type partial differential equations. It evolves the cell averages of the physical solution and its moments (a feature of Hermite WENO) while discretizes high order spatial derivatives using the local DG method. The new scheme has the advantages of both LDG and HWENO methods, including the ability to deal with high order spatial derivatives and the use of a small number of global unknown variables. The latter is independent of the order of the scheme and the spatial order of the underlying differential equations. One and two dimensional numerical examples are presented to show that the scheme can attain the same formal high order accuracy as the LDG method.

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