TY - JOUR
T1 - Finite Volume Hermite WENO Schemes for Solving the Hamilton-Jacobi Equation
AU - Jun Zhu & Jianxian Qiu
JO - Communications in Computational Physics
VL - 4
SP - 959
EP - 980
PY - 2014
DA - 2014/04
SN - 15
DO - http://doi.org/10.4208/cicp.120313.230813s
UR - https://global-sci.org/intro/article_detail/cicp/7122.html
KW - 
AB - <p style="text-align: justify;">In this paper, we present a new type of Hermite weighted essentially non-oscillatory
(HWENO) schemes for solving the Hamilton-Jacobi equations on the finite
volume 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 time
approaching and used in the reconstructions. And the major advantages of the new
HWENO schemes are their compactness in the spacial field, purely on the finite volume
framework and only one set of small stencils is used for different type of the
polynomial reconstructions. Extensive numerical tests are performed to illustrate the
capability of the methodologies.</p>