AN OSCILLATION-FREE DISCONTINUOUS GALERKIN METHOD FOR SCALAR HYPERBOLIC CONSERVATION LAWS

doi:10.1137/20M1354192

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	AN OSCILLATION-FREE DISCONTINUOUS GALERKIN METHOD FOR SCALAR HYPERBOLIC CONSERVATION LAWS
	Lu, Jianfang 1; Liu, Yong 2; Shu, Chi-Wang 3
	2021
发表期刊	SIAM JOURNAL ON NUMERICAL ANALYSIS
ISSN	0036-1429
卷号	59 期号:3 页码:1299-1324
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.
关键词	hyperbolic conservation laws discontinuous Galerkin nonoscillatory optimal error estimates superconvergence
DOI	10.1137/20M1354192
收录类别	SCI
语种	英语
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
WOS类目	Mathematics, Applied
WOS记录号	WOS:000674273400006
出版者	SIAM PUBLICATIONS
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/59087
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.South China Res Ctr Appl Math & Interdisciplinar, Guangzhou 510631, Guangdong, Peoples R China 2.Chinese Acad Sci, Hua Loo Keng Ctr Math Sci, Acad Math & Syst Sci, Beijing 100190, Peoples R China 3.Brown Univ, Div Appl Math, Providence, RI 02912 USA
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.