A Generalization of a Troubled-Cell Indicator to $h$-Adaptive Meshes for Discontinuous Galerkin Methods
Year: 2020
Author: Hongqiang Zhu, Wenxiu Han, Haijin Wang
Advances in Applied Mathematics and Mechanics, Vol. 12 (2020), Iss. 5 : pp. 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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/aamm.OA-2019-0149
Advances in Applied Mathematics and Mechanics, Vol. 12 (2020), Iss. 5 : pp. 1224–1246
Published online: 2020-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 23
Keywords: Troubled-cell indicator discontinuous Galerkin method adaptive mesh conservation law.
Author Details
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