@Article{AAMM-12-5,
author = {Zhu, Hongqiang and Wenxiu, Han and Wang, Haijin},
title = {A Generalization of a Troubled-Cell Indicator to $h$-Adaptive Meshes for Discontinuous Galerkin Methods},
journal = {Advances in Applied Mathematics and Mechanics},
year = {2020},
volume = {12},
number = {5},
pages = {1224--1246},
abstract = {<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>},
issn = {2075-1354},
doi = {https://doi.org/10.4208/aamm.OA-2019-0149},
url = {https://global-sci.com/article/73074/a-generalization-of-a-troubled-cell-indicator-to-h-adaptive-meshes-for-discontinuous-galerkin-methods}
}