  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.
