A hybrid LDG-HWENO scheme for KdV-type equations

TL;DR

This paper introduces a hybrid LDG-HWENO numerical scheme for KdV-type equations that combines advantages of both methods, achieving high order accuracy with fewer global unknowns.

Contribution

A novel hybrid LDG-HWENO scheme that efficiently handles high order derivatives and reduces global unknowns for KdV equations.

Findings

Achieves high order accuracy comparable to LDG methods.

Effectively handles high order spatial derivatives.

Uses fewer global unknown variables regardless of scheme order.

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.