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

被引:3
|
作者
Zhu, Hongqiang [1 ]
Qiu, Jianxian [2 ]
机构
[1] Nanjing Univ Posts & Telecommun, Sch Nat Sci, Nanjing 210023, Jiangsu, Peoples R China
[2] Xiamen Univ, Sch Math Sci, Xiamen 361005, Fujian, Peoples R China
关键词
Runge-Kutta discontinuous Galerkin method; h-adaptive method; Hamilton-Jacobi equation; FINITE-ELEMENT-METHOD; ESSENTIALLY NONOSCILLATORY SCHEMES; HERMITE WENO SCHEMES; SHOCK-CAPTURING SCHEMES; WEIGHTED ENO SCHEMES; CONSERVATION-LAWS; EFFICIENT IMPLEMENTATION; PART I; LIMITERS; SYSTEMS;
D O I
10.4208/nmtma.2013.1235nm
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
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.
引用
收藏
页码:617 / 636
页数:20
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