TY - JOUR
T1 - A Generalization of a Troubled-Cell Indicator to $h$-Adaptive Meshes for Discontinuous Galerkin Methods
AU - Zhu , Hongqiang
AU - Han , Wenxiu
AU - Wang , Haijin
JO - Advances in Applied Mathematics and Mechanics
VL - 5
SP - 1224
EP - 1246
PY - 2020
DA - 2020/07
SN - 12
DO - http://doi.org/10.4208/aamm.OA-2019-0149
UR - https://global-sci.org/intro/article_detail/aamm/17746.html
KW - Troubled-cell indicator, discontinuous Galerkin method, adaptive mesh, conservation law.
AB - <p style="text-align: justify;">We generalize the troubled-cell indicator on unstructured triangular meshes recently introduced by Fu and Shu (J. Comput. Phys., 347 (2017), pp. 305--327) to $h$-adaptive rectangular meshes where hanging nodes exist. The generalized troubled-cell indicator keeps the good properties of simplicity, compactness and insensitivity to particular test cases. Numerical tests on the two-dimensional scalar Burgers&#39; equation and hyperbolic systems of Euler equations demonstrate the good performance of the generalized indicator. The results on both uniform and $h$-adaptive meshes indicate that the generalized indicator is able to capture shocks effectively without any PDE-sensitive parameter to tune.</p>