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An h-Adaptive Runge-Kutta Discontinuous Galerkin Method for Hamilton-Jacobi Equations

Published online by Cambridge University Press:  28 May 2015

Hongqiang Zhu  and
Jianxian Qiu
Hongqiang Zhu*
Affiliation:
School of Natural Science, Nanjing University of Posts and Telecommunications, Nanjing 210023, Jiangsu, China
Jianxian Qiu*
Affiliation:
School of Mathematical Sciences, Xiamen University, Xiamen 361005, Fujian, China
*
Corresponding author.Email address:zhuhq@njupt.edu.en
Corresponding author.Email address:jxqiu@xmu.edu.en
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Abstract

In [35,36], we presented an h-adaptive Runge-Kutta discontinuous Galerkin method using troubled-cell indicators for solving hyperbolic conservation laws. A tree data structure (binary tree in one dimension and quadtree in two dimensions) is used to aid storage and neighbor finding. Mesh adaptation is achieved by refining the troubled cells and coarsening the untroubled “children”. Extensive numerical tests indicate that the proposed h-adaptive method is capable of saving the computational cost and enhancing the resolution near the discontinuities. In this paper, we apply this h-adaptive method to solve Hamilton-Jacobi equations, with an objective of enhancing the resolution near the discontinuities of the solution derivatives. One- and two-dimensional numerical examples are shown to illustrate the capability of the method.

Keywords

65M6065M9935L65Runge-Kutta discontinuous Galerkin methodh-adaptive methodHamilton-Jacobi equation
Type
Research Article
Information
Numerical Mathematics: Theory, Methods and Applications , Volume 6 , Issue 4 , November 2013 , pp. 617 - 636
Copyright
Copyright © Global Science Press Limited 2013

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