Finite Volume Hermite WENO Schemes for Solving the Hamilton-Jacobi Equation (Communications in Computational Physics, 2020)
In this paper, we present a new type of Hermite weighted essentially non-oscillatory(HWENO) schemes for solving the Hamilton-Jacobi equations on the finitevolume framework. The cell averages of the function and its first one (in one dimension)or two (in two dimensions) derivative values are together evolved via timeapproaching and used in the reconstructions. And the major advantages of the newHWENO schemes are their compactness in the spacial field, purely on the finite volumeframework and only one set of small stencils is used for different type of thepolynomial reconstructions. Extensive numerical tests are performed to illustrate thecapability of the methodologies.