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Volume 15, Issue 4
Finite Volume Hermite WENO Schemes for Solving the Hamilton-Jacobi Equation

Jun Zhu & Jianxian Qiu

DOI: 10.4208/cicp.120313.230813s

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

Published online: 2014-04

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  • 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.

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@Article{CiCP-15-959, author = {Jun Zhu and Jianxian Qiu}, title = {Finite Volume Hermite WENO Schemes for Solving the Hamilton-Jacobi Equation}, journal = {Communications in Computational Physics}, year = {2014}, volume = {15}, number = {4}, pages = {959--980}, 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.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.120313.230813s}, url = {http://global-sci.org/intro/article_detail/cicp/7122.html} }
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 -

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.

Jun Zhu and Jianxian Qiu. (2014). Finite Volume Hermite WENO Schemes for Solving the Hamilton-Jacobi Equation. Communications in Computational Physics. 15 (4). 959-980. doi:10.4208/cicp.120313.230813s
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