@Article{NMTMA-6-617,
author = {Hongqiang Zhu and Jianxian Qiu},
title = {An $h$-Adaptive Runge-Kutta Discontinuous Galerkin Method for Hamilton-Jacobi Equations},
journal = {Numerical Mathematics: Theory, Methods and Applications},
year = {2013},
volume = {6},
number = {4},
pages = {617--636},
abstract = {<p style="text-align: justify;">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
&quot;children&quot;. 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.</p>},
issn = {2079-7338},
doi = {https://doi.org/10.4208/nmtma.2013.1235nm},
url = {http://global-sci.org/intro/article_detail/nmtma/5922.html}
}