AN OSCILLATION-FREE DISCONTINUOUS GALERKIN METHOD FOR SCALAR HYPERBOLIC CONSERVATION LAWS
文献类型：期刊论文
| 作者 | Lu, Jianfang3; Liu, Yong2; Shu, Chi-Wang1 |
| 刊名 | SIAM JOURNAL ON NUMERICAL ANALYSIS
 |
| 出版日期 | 2021 |
| 卷号 | 59期号:3页码:1299-1324 |
| 关键词 | hyperbolic conservation laws discontinuous Galerkin nonoscillatory optimal error estimates superconvergence |
| ISSN号 | 0036-1429 |
| DOI | 10.1137/20M1354192 |
| 英文摘要 | In this paper, we propose a novel discontinuous Galerkin (DG) method to control the spurious oscillations when solving the scalar hyperbolic conservation laws. Usually, the high order linear numerical schemes would generate spurious oscillations when the solution of the hyperbolic conservation laws contains discontinuities. The spurious oscillations may be harmful to the numerical simulation, as it not only generates some artificial structures not belonging to the problems, but also causes many overshoots and undershoots that make the numerical scheme less robust. To overcome this difficulty, in this paper we introduce a numerical damping term to control spurious oscillations based on the classic DG formulation. In comparison to the classic DG method, the proposed DG method still maintains many good properties, such as the extremely local data structure, conservation, L-2-boundedness, optimal error estimates, and superconvergence. We also provide some numerical examples to show the good performance of the proposed DG scheme and verify our theoretical results. |
| 资助项目 | National Natural Science Foundation of China[11901213] ; Guangdong Basic and Applied Basic Research Foundation[2020B1515310021] ; China Postdoctoral Science Foundation[2020TQ0343] ; NSF[DMS-2010107] ; AFOSR[FA9550-20-1-0055] |
| WOS研究方向 | Mathematics |
| 语种 | 英语 |
| WOS记录号 | WOS:000674273400006 |
| 出版者 | SIAM PUBLICATIONS |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/59086]  |
| 专题 | 中国科学院数学与系统科学研究院 |
| 通讯作者 | Lu, Jianfang |
| 作者单位 | 1.Brown Univ, Div Appl Math, Providence, RI 02912 USA 2.Chinese Acad Sci, Hua Loo Keng Ctr Math Sci, Acad Math & Syst Sci, Beijing 100190, Peoples R China 3.South China Res Ctr Appl Math & Interdisciplinar, Guangzhou 510631, Guangdong, Peoples R China |
| 推荐引用方式 GB/T 7714 | Lu, Jianfang,Liu, Yong,Shu, Chi-Wang. AN OSCILLATION-FREE DISCONTINUOUS GALERKIN METHOD FOR SCALAR HYPERBOLIC CONSERVATION LAWS[J]. SIAM JOURNAL ON NUMERICAL ANALYSIS,2021,59(3):1299-1324. |
| APA | Lu, Jianfang,Liu, Yong,&Shu, Chi-Wang.(2021).AN OSCILLATION-FREE DISCONTINUOUS GALERKIN METHOD FOR SCALAR HYPERBOLIC CONSERVATION LAWS.SIAM JOURNAL ON NUMERICAL ANALYSIS,59(3),1299-1324. |
| MLA | Lu, Jianfang,et al."AN OSCILLATION-FREE DISCONTINUOUS GALERKIN METHOD FOR SCALAR HYPERBOLIC CONSERVATION LAWS".SIAM JOURNAL ON NUMERICAL ANALYSIS 59.3(2021):1299-1324. |
入库方式： OAI收割
来源：数学与系统科学研究院
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