Commun. Comput. Phys., 15 (2014), pp. 959-980.


Finite Volume Hermite WENO Schemes for Solving the Hamilton-Jacobi Equation

Jun Zhu 1, Jianxian Qiu 2*

1 College of Science, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, Jiangsu, China.
2 School of Mathematical Sciences, Xiamen University, Xiamen 361005, Fujian, China.

Received 12 March 2013; Accepted (in revised version) 23 August 2013
Available online 21 January 2014
doi:10.4208/cicp.120313.230813s

Abstract

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.

AMS subject classifications: 65M06, 65M99, 35L65

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Key words: HWENO scheme, finite volume, Hamilton-Jacobi equation.

*Corresponding author.
Email: zhujun@nuaa.edu.cn (J. Zhu), jxqiu@xmu.edu.cn (J. Qiu)
 

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