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

doi:10.1137/20M1354192

	AN OSCILLATION-FREE DISCONTINUOUS GALERKIN METHOD FOR SCALAR HYPERBOLIC CONSERVATION LAWS
	Lu, Jianfang 3; Liu, Yong 2; Shu, Chi-Wang 1
刊名	SIAM JOURNAL ON NUMERICAL ANALYSIS
	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
出版者	SIAM PUBLICATIONS
WOS记录号	WOS:000674273400006
内容类型	期刊论文
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.