@Article{AAMM-12-1224, author = {Zhu , HongqiangHan , Wenxiu 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 = {

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' 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.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.OA-2019-0149}, url = {http://global-sci.org/intro/article_detail/aamm/17746.html} }