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An Arbitrary-Order Discontinuous Galerkin Method with One Unknown Per Element
Li, Ruo1,2; Ming, Pingbing3,4; Sun, Ziyuan2; Yang, Zhijian5
2019-07-01
Source PublicationJOURNAL OF SCIENTIFIC COMPUTING
ISSN0885-7474
Volume80Issue:1Pages:268-288
AbstractWe propose an arbitrary-order discontinuous Galerkin method for second-order elliptic problem on general polygonal mesh with only one degree of freedom per element. This is achieved by locally solving a discrete least-squares over a neighboring element patch. Under a geometrical condition on the element patch, we prove an optimal a priori error estimates in the energy norm and in the L2 norm. The accuracy and the efficiency of the method up to order six on several polygonal meshes are illustrated by a set of benchmark problems.
KeywordLeast-squares reconstruction Discontinuous Galerkin method Elliptic problem
DOI10.1007/s10915-019-00937-y
Language英语
Funding ProjectNational Natural Science Foundation of China[11425106] ; National Natural Science Foundation of China[91630313] ; National Natural Science Foundation of China[11671312]
WOS Research AreaMathematics
WOS SubjectMathematics, Applied
WOS IDWOS:000468983100010
PublisherSPRINGER/PLENUM PUBLISHERS
Citation statistics
Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/34911
Collection计算数学与科学工程计算研究所
Corresponding AuthorMing, Pingbing
Affiliation1.Peking Univ, LMAM, CAPT, Beijing 100871, Peoples R China
2.Peking Univ, Sch Math Sci, Beijing 100871, Peoples R China
3.Chinese Acad Sci, Acad Math & Syst Sci, LSEC, 55 Zhong Guan Cun East Rd, Beijing 100190, Peoples R China
4.Univ Chinese Acad Sci, Sch Math Sci, 19A Yu Quan Rd, Beijing 100049, Peoples R China
5.Wuhan Univ, Sch Math & Stat, Wuhan 430072, Hubei, Peoples R China
Recommended Citation
GB/T 7714
Li, Ruo,Ming, Pingbing,Sun, Ziyuan,et al. An Arbitrary-Order Discontinuous Galerkin Method with One Unknown Per Element[J]. JOURNAL OF SCIENTIFIC COMPUTING,2019,80(1):268-288.
APA Li, Ruo,Ming, Pingbing,Sun, Ziyuan,&Yang, Zhijian.(2019).An Arbitrary-Order Discontinuous Galerkin Method with One Unknown Per Element.JOURNAL OF SCIENTIFIC COMPUTING,80(1),268-288.
MLA Li, Ruo,et al."An Arbitrary-Order Discontinuous Galerkin Method with One Unknown Per Element".JOURNAL OF SCIENTIFIC COMPUTING 80.1(2019):268-288.
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