Year: 2013
Numerical Mathematics: Theory, Methods and Applications, Vol. 6 (2013), Iss. 4 : pp. 617–636
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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/nmtma.2013.1235nm
Numerical Mathematics: Theory, Methods and Applications, Vol. 6 (2013), Iss. 4 : pp. 617–636
Published online: 2013-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 20
Keywords: Runge-Kutta discontinuous Galerkin method h-adaptive method Hamilton-Jacobi equation.
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An h-Adaptive RKDG Method for the Two-Dimensional Incompressible Euler Equations and the Guiding Center Vlasov Model
Zhu, Hongqiang
Qiu, Jianxian
Qiu, Jing-Mei
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https://doi.org/10.1007/s10915-017-0440-9 [Citations: 7]