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Central discontinuous Galerkin methods on overlapping meshes for wave equations
Liu, Yong1; Lu, Jianfang2; Shu, Chi-Wang3; Zhang, Mengping4
2021-02-18
Source PublicationESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE
ISSN0764-583X
Volume55Issue:1Pages:329-356
AbstractIn this paper, we study the central discontinuous Galerkin (DG) method on overlapping meshes for second order wave equations. We consider the first order hyperbolic system, which is equivalent to the second order scalar equation, and construct the corresponding central DG scheme. We then provide the stability analysis and the optimal error estimates for the proposed central DG scheme for one- and multi-dimensional cases with piecewise P-k elements. The optimal error estimates are valid for uniform Cartesian meshes and polynomials of arbitrary degree k >= 0. In particular, we adopt the techniques in Liu et al. (SIAM J. Numer. Anal. 56 (2018) 520-541; ESAIM: M2AN 54 (2020) 705-726) and obtain the local projection that is crucial in deriving the optimal order of convergence. The construction of the projection here is more challenging since the unknowns are highly coupled in the proposed scheme. Dispersion analysis is performed on the proposed scheme for one dimensional problems, indicating that the numerical solution with P-1 elements reaches its minimum with a suitable parameter in the dissipation term. Several numerical examples including accuracy tests and long time simulation are presented to validate the theoretical results.
KeywordOptimal error estimates central DG method second order wave equation dispersion analysis
DOI10.1051/m2an/2020069
Indexed BySCI
Language英语
Funding ProjectChina Scholarship Council ; China Postdoctoral Science Foundation[2020TQ0343] ; NSFC[11871448] ; NSFC[11901213] ; NSF[DMS-1719410] ; NSF[DMS-2010107] ; AFOSR[FA9550-20-1-0055]
WOS Research AreaMathematics
WOS SubjectMathematics, Applied
WOS IDWOS:000619239500012
PublisherEDP SCIENCES S A
Citation statistics
Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/58186
Collection中国科学院数学与系统科学研究院
Corresponding AuthorLu, Jianfang
Affiliation1.Chinese Acad Sci, Acad Math & Syst Sci, Hua Loo Keng Ctr Math Sci, Beijing 100190, Peoples R China
2.South China Normal Univ, South China Res Ctr Appl Math & Interdisciplinary, Guangzhou 510631, Guangdong, Peoples R China
3.Brown Univ, Div Appl Math, Providence, RI 02912 USA
4.Univ Sci & Technol China, Sch Math Sci, Hefei 230026, Anhui, Peoples R China
Recommended Citation
GB/T 7714
Liu, Yong,Lu, Jianfang,Shu, Chi-Wang,et al. Central discontinuous Galerkin methods on overlapping meshes for wave equations[J]. ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE,2021,55(1):329-356.
APA Liu, Yong,Lu, Jianfang,Shu, Chi-Wang,&Zhang, Mengping.(2021).Central discontinuous Galerkin methods on overlapping meshes for wave equations.ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE,55(1),329-356.
MLA Liu, Yong,et al."Central discontinuous Galerkin methods on overlapping meshes for wave equations".ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE 55.1(2021):329-356.
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