TY - JOUR
T1 - An $h$-Adaptive Runge-Kutta Discontinuous Galerkin Method for Hamilton-Jacobi Equations
AU - Hongqiang Zhu & Jianxian Qiu
JO - Numerical Mathematics: Theory, Methods and Applications
VL - 4
SP - 617
EP - 636
PY - 2013
DA - 2013/06
SN - 6
DO - http://doi.org/10.4208/nmtma.2013.1235nm
UR - https://global-sci.org/intro/article_detail/nmtma/5922.html
KW - Runge-Kutta discontinuous Galerkin method, h-adaptive method, Hamilton-Jacobi equation.
AB - <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>